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ASTRONOMY. 



General 
View. 



Lstronomy. Astronomy (formed of aarpov, a star, and vofio^, 
— V— »^ law,) is a mixed mathematical science, which treats 
of the heavenly bodies, their motions, periods, eclip- 
ses, magnitudes, &c. and of the causes on which they 
depend. That part of the science which relates to 
the motions, magnitudes, and periods of revolutions, 
is denominated pure astronomy ; and that which inves- 
tigates the causes of those motions, and the laws by 
which they are regulated, is called physical astronomy. 

§ I. History of Astronomy. 

It would be useless, if even the nature of our work 
would admit of it, to attempt to trace the history of 
this science from its earliest state of infancy, which is 
probably nearly coeval with that of society itself j 
at least if we regard the rude observations of shep- 
herds and herdsmen as exhibiting the first dawn of 
astronomy. A man must be strangely divested of the 
curiosity peculiar to his species, who, while exposed 
to the varying canopy of the heavens, thi'ough suc- 
cessive nights and seasons, could suffer such a 
brilliant spectacle to pass repeatedly before him, 
Avithout noticing the fixed or variable objects there 
presented to his view ; and his attention, once drawn 
to a contemplation of the firmament, he would re- 
mark the invariable position of the greater number 
of those bodies with regard to each other ; the irre- 
gular motion of others ; and hence, by some deno- 
mination or other, we should have a distinction 
made between what we now call the jftxed stars and 
the planets ; while the sun and moon are in, their ap- 
pearances sufficiently distinct from the rest of the 
heavenly bodies, to have called for a farther distin- 
guishing appellation, and to have claimed the parti- 
cular regard of these rude observers. 

Such was probably the origin of astronomy ; and 
in this state, in all likelihood, it might remain for 
many ages, and in many countries unknown to and 
unconnected with each other. The length of the 
year, the duration of a lunar revolution, the particular 
rising of certain stars at certain seasons, and a few 
other common and obvious phenomena, might 
therefore be predicted Avith a certain degree of accu- 
racy, long before those observations assumed any 
thing like a scientific form, and long anterior to that 
time from which we date the origin of astronomy as 
a science, properly so called. 

The hon(>- "^ being the first inventors of this 
sublime "'-S en attributed to various nations ; 

^™ gyptians, the Chinese, the In- 

-~*^" I their advocates amongst our 

5 ; and even a certain unknown 

■.ed by the enthvisiasm of some 

traces are supposed to have 

whom all original knowledge 

een attributed. The more 



Claims of 
ihe Chalde- 
iins, &c. li 



closely, however, we examine the claims of these History', 
actual or imaginary people, the more we shall be ^— ^y-lu^ 
convinced that their astronomy consisted of little 
more than we have indicated above ; viz. a tolerable 
approximation to certain periods, and to the re-appear- 
ance of certain phenomena, that required nothing 
more than a continued and patient observation of 
stated occurrences, which as we have observed, 
could not long remain unnoticed even in the most 
infant state of society. 

We may judge of the state of Egj'ptian astronomy Egyptians. 
from the circumstance of Thales having first taught 
them how to find the heights of the pyramids from 
the length of their shadows. It is true that they had 
some idea of the length of the year, and had, in a 
certain measure, approximated towards a determina- 
tion of the obliquity of the ecliptic, or of the path of 
the sun, which they stated to be 24°. The Chaldeans 
appear to have made some rude observations on 
eclipses, but still little scientific knowledge can be 
attributed to this people ; who after observing these 
phenomena, were contented to explain them by 
teaching that the two great luminaries of the hea- 
vens were only on fire on one side, and that eclipses 
were occasioned by the accidental turning of their 
dark sides towards us. And again, that these bodies 
were carried round the heavens in chariots, close on 
all sides except one, in which there was a round 
hole, and that a total or partial eclipse was occasioned 
by the complete or partial shutting of this aperture. 
Similar absurd and extravagant notions will be 
found amongst all the early pretenders to the study 
of astronomy ; but we cannot concede to such know- 
ledge and pretences the term science ; they had in 
fact no science, they had amassed together a num- 
ber of rude observations, and had been thus enabled 
to determine certain periods, and to predict some few 
phenomena ; but we have no proof, nor even any 
reason whatever to imagine, from any facts that have 
been handed down to us, that these predictions 
rested upon any other basis than that of simply 
observing, the repeated returns of these appearances 
within certain periods. 

If to the knowledge above indicated, we add an Astronomy 
arbitrary collection of certain clusters or groups of as it was re- 
stars into constellations ; the division of the zodiac [^^ ^.^^j^^ 
into twelve signs, corresponding to the twelve months Greeks. 
of the year J into twenty-seven or twenty-eight 
hours, answering to the daily motion of the moon ; 
an obscure idea of the revolution of the earth upon its 
axis, which was afterwards lost ; a knowledge of five 
planets ; and some contradictory notions respecting 
the nature and motion of comets, we shall have a 
pretty correct picture of the state of astronomy as it 
was received amongst the Greeks ; and from whom it 
first derived its scientific character. It is therefore 
3 R 



48G 



ASTRONOMY. 






>'. only from this period that we shall commence our 
historical sketch, and attempt to trace the rise and 
progress of astronomy. 
Successive ^^^ shall follow it, from the state above described, 
periods in when every thing depended upon observation only, 
the liistory unaided either by a calculus or instruments ; throiigh 
of astrono- ^^lat in which the latter began to be employed, and 
some assistance was derived from the more elemen- 
tary positions of geometry. We shall next examine 
■^^- it from the period when astronomical science was 

enriched and extended by the invention of the tele- 
scope, but while the principles of computations were 
still founded on the elements of pure geometry ; and 
lastly, we shall exhibit the science as it now exists, 
supported by every aid that can be derived from the 
present high state of practical and theoretical mecha- 
nics and optics ; when the effect of every celestial 
motion, and every disturbing force is made to depend 
upon one universal law ; and the amount of each 
investigated and submitted to computation, by means 
of the powerful assistance derived from the modern 
analysis. 

The first period above alluded to, comprehends a 
long series of ages, during which the science of 
astronomy passed into the hands of different people 
and nations. First, to the Greeks, then to the Arabs ; 
from which latter it seems probable that it found its 
way to India and China, about the same time that it 
was also brought into Spain ; whence it afterwards 
spread throughout all parts of civilized Europe. We 
shall therefore divide this period into the following 
minor sections. The astronomy of the Greeks ; of 
the Arabs ; of the Indians and Chinese ; and of mo- 
dern Europe ; which latter will bring us up to the time 
of Copernicus and Galileo ; including, in all, about 
twenty-one centuries. 

Of the Astronomy of the Greeks. 
Thales. Thales is generally considered as the founder of 

B. c, b'OO. astronomy amongst the Greeks. This philosopher, 
who must have flourished about 600 years before the 
commencement of the Christian sera, is said to have 
taught that the stars were fire, or that they shone by 
mieans of their own light ; the moon received her 
light from the sun, and that she became invisible in 
her conjunctions, in consequence of being hidden or 
absorbed in the solar rays, which it must be acknow- 
ledged is but an obscure way of saying that she then 
turned towards us her unenlightened hemisphere. He 
taught farther that the earth is spherical, and placed 
in the centre of the world ; he divided the heavens, 
or rather found them divided into five circles, the 
equator, the two tropics, and the arctic and antarctic 
circles. The year he made to consist of 365 days ; 
and determined " the motion of the sun in declina- 
tion." What is meant by this expression is not very 
easy to comprehend ; if it only means that he disco- 
vered such a motion, it can scarcely be considered as 
correct, as it must have been known prior to his 
time ; viz. to the first observers ; and it cannot mean 
that he laid down rules for computing it, as we have 
every reason to know that the most simple principles 
of trigonometry were not propagated till many cen- 
turies after his time. 
Predict an Thales is also said to have first observed an eclipse, 
eclipse. and to have predicted that celebrated one which 



temiinated the war between the Medes and the History; 
Lydians ; an eclipse on which much has been written, V«-^^^-i^ 
but from which very little satisfactory information 
has been obtained. Herodotus says, " it happened 
that the day was changed suddenly into night, a 
change which Thales the Milesian had announced to 
the people of Ionia, assigning for the limit of his pre- 
diction, the year in which the change actually took 
place." Thales had therefore neither predicted the 
day nor the month ; and in all probability he had 
no other principle to proceed upon, than the Chaldean 
period of eclipses already alluded to in the preceding 
part of this article. 

The pointed declaration of the historian, that the 
limits assigned by the astronomer for the appearance 
of this phenomenon, was the year in which it hap- 
pened, is a pretty obvious proof of the low state of 
astronomical science at this time, and it would be of 
little importance whether the eclipse w"as itself partial 
or total ; but as there is little doubt that such an 
event actually took place, it becomes a matter of 
high importance in chronology, to ascertain whether 
it was such as it is described, viz. a total eclipse ; for 
no partial obscuration of the sun's light would accord 
with the description of Herodotus, of the day being 
suddenly changed into night; and such a phenomenon 
in any particular place being an extremely rare occur- 
rence, it would, if correct, enable us to determine 
not only the year, but tlie very day and hour at 
which it happened, and thus furnish at least one indis- 
putable period in chronology and history. 

Various dates have been assigned to this eclipse. Dates as- 
Pliny places it in the fourth year of the forty-eighth signed to 
Olympiad which answers to the year 585 b. c. fHist. ""^ ^"'P^®' 
Nat. lib. 2. cap. 12.), a similar opinion has been ad- 
vanced by Cicero fDe Divinat. lib. 1. § 49.) and pro- 
bably by Eudemus (Clement. Alex. Strom, lib. 1. p. 
354.); by Newton fChron. of Anc. Kings amendedj ; 
Riccioli (Chron. Reform, vol. 1. p. 228.) ; Desvignoles 
(Chronol. lib. 4. cap. 5. § 7, &c.) ; and by Brosses 
{M^m. de VAcad. des Belles Lettres, torn. 21. Mem. p. 
33.) 

Scaliger, in two of his writings, CAnimad. ad Euseb. 
p. 89.) and in (OXv/j,. dva^/pacpy) has adopted also the 
opinion of Pliny ; but in another work fDe Emen. 
Temp, in Can. Isag. p. 321.) he fixes the date of this 
eclipse to the 1st of October, 583, b. c. Calvisius 
states it in his (Opus Chron. J to have taken place in 
607 B. c. Petavius says it happened July 9th, 597 
B. c. (De Doct. Temp. lib. 10. cap. 1.) which date has 
likewise been adopted by Marsham, Bouhier, Corsini ; 
and by M. Larcher the French translator of Hero- 
dotus, (tom. i. p. 335.) Usher is of opinion that it 
happened 601 b. c. ; and Bayer, May 18, 603, b. c. ; 
which latter opinion has been supported by two 
English astronomers. Costard and Stukeley, (Phil. 
Trans, for 1753.) But Volney attempts to show in 
his (Chronologie d'HerodoteJ that it could be no other 
than the eclipse which happened February 3d, 626 

B.C. 

Mr. F. Bailly has examined with great care and 
labour the probability of these several statements, 
from which it appears, that most of the eclipses above 
alluded to happened under circumstances which ren- 
der it absolutely impossible any of them should be 
that alluded to by Herodotus ; most of them were 



ASTRONOMY. 



487 



1 



naxagoras. 
B.C. 530, 



Astronomy, ^ot even visible in that country, which must necessa- 
t _.- i_ > rily have been the scene of action between the Medes 
and the Lydians, and none of them was total in those 
places. He has therefore with great perseverance, by 
means of the last new astronomical tables of the 
Bureau des Longitudes, computed backward to find 
whether any eclipse of the sun actually happened 
within the probable limits of the event recorded by 
the historian, and the result of his I'esearch is, that 
on the 10th of September, 610 b. c, there was a 
solar eclipse, which was total in some parts of Asia 
Minor ; and which, he therefore concludes, with great 
probability, was the identical one referred to by 
Herodotus. Admitting, therefore, the conclusion, 
we have one decided point of time to which we are 
enabled to refer with conlidence, and at which time, 
the state of astronomy is known to have been such as 
we have described. See Phil. Trans, for 1811. 
Anaximan- The successors of Thales, Anaximander, Anaxima- 
der, Anaxi- nes. and Anaxagoras, contributed considerably to the 
manes. A- advancement of astronomy. The first is said to have 
invented or introduced the gnomon into Greece ; to 
have observed the obliquity of the ecliptic ; and taught 
that the earth was spherical, and the centre of the 
universe, and that the sun was not less than it. He 
is also said to have made the first globe, and to have 
set up a sun-dial at Laced aemon, which is the first we 
hear of among the Greeks ; though some are of opi- 
nion that these pieces of knowledge Avere brought from 
Babylon by Pherecydes, a contemporary of Anaximan- 
der. Anaxagoras also predicted an eclipse which 
happened in the fifth year of the Peloponnesian war ; 
and taught that the moon Avas habitable, consisting of 
hills, A'^alleys, and waters, like the earth. His contem- 
Pythagoras. porary Pythagoras, however, greatly improved not 
B.C. 540. only astronomy and mathematics, but every other 
branch of philosophy. He taught that the universe 
was composed of four elements, and that it had the 
sun in the centre ; that the earth was round, that we had 
antipodes ; and that the moon reflected the rays of 
the sun ; that the stars were worlds, containing earth, 
air, and ether ; that the moon was inhabited like the 
earth ; and that the comets were a kind of wandering 
stars, disappearing in the superior parts of their orbits, 
and becoming visible only in the lower parts of them. 
The white colour of the milky-way he ascribed to the 
brightness of a great number of small stars ; and he 
supposed the distances of the moon and planets from 
the earth to be in certain harmonic proportion to one 
another. He is said also to have exhibited the ob- 
lique course of the sun in the ecliptic and the tropical 
circles, by means of an artificial sphere ; and he first 
taught that the planet Venus is both the evening and 
morning star. This philosopher is said to have been 
taken prisoner by Cambyses, and thus to have become 
acquainted with all the mysteries of the Persian magi ; 
after which he settled at Crotona in Italy, and founded 
the Italian sect. 
Philolaus. About 440 years before the Christian sera, Philolaus, 
B. 0. a celebrated Pythagorean, asserted the annual motion 
440-432. of the earth round the sun ; and soon after Hicetas, a 
Syracusan, taught its diurnal motion on its own axis. 
About this time also flourished Meton and Euctemon 
at Athens, Avho took an exact observation of the sum- 
mer solstice 432 years before Christ ; which is the 
oldest observation of the kind we have^ excepting 



History. 



some doubtful ones of the Chinese. Meton is said to 
have composed a cycle of 19 years, which still bears v 
his name ; and he marked the risings and settings of 
the stars, and what seasons they pointed out : in all 
of which he was assisted by his companion Eucte- 
mon. The science, however, was obscured by Plato 
and Aristotle, who embraced the system afterwards 
called the Ptolemaic, which places the earth in the 
centre of the universe. 

After Philolaus, the next astronomer we meet with Eudoxus. 
of great reputation is Eudoxus, who flourished 3/0 b.c. b.c. 370. 
Pie Avas a contemporary Avitli Aristotle though con- 
siderably older, and is greatly celebrated for his skill 
in this science. Pie is said to have been the first to 
apply geometry to astronomy, and is supposed to be 
the inventor of many of the propositions attributed to 
Euclid. Having travelled into Egypt in the early 
part of his life, he obtained a recommendation from 
Agesilaus to Nectanebus, king of Egypt, and by his 
means got access to the priests, Avho Avere then held 
to have great knoAvledge of astronomy ; after Avhich 
he taught in Asia and Italy. Seneca tells us, that 
he brought the knowledge of astronomy, i. e. of the 
planetary motions, from Egypt into Greece : and 
according to Archimedes, his opinion Avas, that the 
diameter of the sun Avas nine times that of the moon. 
He Avas also acquainted, with the method of draAving 
a sun dial on a plane. 

Soon after Eudoxus, we meet with Callippus, whose Callippus. 
system of the celestial sphere is mentioned by Ari- b.c. 330. 
stotle ; but he is better knoAvn for a period of 76 
years, containing four corrected Metonic periods, and 
which had its beginning at the summer solstice, in 
the year 330 b. c. And it was about this time, or 
rather earlier, that the Greeks having begun to 
plant colonies in Italy, Gaul, and Egypt, became ac- 
quainted with the Pythagorean system, and the notions 
of the ancient Druids concerning astronomy. 

Passing over the names of various other astrono- Autolycus 
mers of this period, Avho appear to have done very b.c. 300, 
little towards the advancement of the science, we 
come to Autolycus, the most ancient Avriter Avhose 
Avorks have been handed doAvn to our time. He 
Avrote two books, viz. Of the Sphere which moves, and 
the other. On the Risings and Settings of the Stars. 
These Avorks Avere composed about 300 b. c. 

We have noAV passed over a period of 300 years 
from the time of Thales, and therefore, by making a 
fcAV extracts from these AVorks of Autolycus, Ave shall 
be enabled to form some idea of the progress of astro- 
nomy during this period. In the work on the move- 
able sphere, we have several propositions, of Avhich 
the folloAAdng are the most important. 

1. If a sphere move uniformly about its axis, all the Earliest 
points on its surface which are not in its axis, AA'ill Work ex- 
describe parallel circles, having for their common tant on As-i 
poles, those of the sphere itself, and of Avhich all the tronomy. 
planes Avill be perpendicular to the axis. 

2. All these points Avill describe, of their respective 
circles, similar arcs in equal times. 

3. Reciprocally, similar arcs Avill indicate equal 
time. 

4. If a great fixed circle, perpendicular to the axis, 
divide the sphere into tAvo hemispheres, the one vi- 
sible, the other invisible, and that the sphere turns 
about its axis ; those points on the surface that are 

3 b2 



488 



ASTRONOMY. 



Remarks 
on tliis 
author. 



Astronomy, hidden, will never rise ; and those that are visible will 
*^— -y— »r^ never set. This is what we now denominate a paral- 
lel sphere ; the great fixed circle corresponding with 
our equator. 

5. If a great circle pass through the poles, all the 
points of the surface will rise and set alternately. 
This corresponds to our horizon, and ,to our right 
sphere. 

6. If the great circle be oblique to the axis, it will 
touch two equal parallel circles ; of which, that adja- 
cent to the one pole will be always apparent, the other 
always invisible. 

The first of these circles was called by the Greeks, 
(although not by this author,) as we still denominate 
it, the arctic circle, and the other tlie antarctic circle. 

7. If the horizon be oblique, the circles, perpendi- 
cular to the axis, will always have their points of rising 
and setting in the same points of the horizon, to 
which they are all equally inclined. 

8. The great circles which touch the arctic and 
antarctic circle, will, during the complete revolution 
of the sphere, twice coincide with the horizon. 

9. In the oblique sphere, of all the points which 
rise at the same instant, those which are nearest to 
the visible pole will set last ; and of the points which 
set at the same instant, those that are nearest the 
same pole will rise first. 

10. In the oblique sphere, every circle which passes 
through the poles, will be perpendicular to the hori- 
zon twice in tlie course of one complete revolution. 

We omit some other propositions of this author, 
which are of less importance than the above ; and 
even those which we have given, are such as one would 
imagine could not have escaped the observation of 
any one who would think of employing an artificial 
sphere to represent the celestial motions ; yet, from 
the tenor of the work in question, it would seem, that 
if they were known, they were never before, at least, 
embodied in the form of a regular treatise. 

Here then we may begin to date the first scientific 
form of astronomy ; because in this work, however 
low and elementary, we have an application of geo- 
metry to illustrate the motions of the heavenly bodies ; 
but we shall still find two other centuries pass away, 
before the same principles were applied to actual 
computation. 

Contemporary with Autolycus, was Euclid ; whose 
B. c. 300, elements of geometry, after so many Jiges, still 
maintain their pre-eminence ; and in which we find all 
the propositions that are necessary for establishing 
' every useful theorem in trigonometry ; yet it is per- 
fectly evident that no ideas were yet conceived of the 
latter science. Neither Euclid nor Archimedes, great 
as were their skill and talents in geometry, had any 
idea of the method of estimating the measure of any 
angle by the arc, which, the t\v-o lines forming it, 
intercepted ; nor does it appear that they knew of any 
instrument whatever for taking angles ; a very con- 
vincing proof of which appears in the process adopted 
by the latter justly celebrated philosopher, in order to 
determine the apparent diameter of the sun. 
Aristarchus Passing over the poet Aratus, who is supposed to 
B. c. 264. have embodied in his poem all the astronomical know- 
ledge of the time in which he wrote, viz. 270 b. c. ; 
but who had not himself made any observations, we 
come to Aristarchus, who has left us a work, entitled 



Euclid. 



Of Magnitudes and Distances; in which he teaches, that History, 
the moon receives her light from the sun, and that —-.^w' 
the earth is only a point in comparison with the sphere 
of the moon. He likewise added, that when the 
moon is dichotomized, we are in the plane of the 
circle which separates the enlightened part from the 
unenlightened, which is the most curious and original 
remark of this author : in this state of the moon, he also 
observes, that the angle subtended by the sun and 
moon, is one-thirtieth less than a right angle ; which, 
in other words, is saying, that the angle is 87°, 
whereas we now know that this angle exceeds 89° SO'. 
In another proposition he asserts, that the breadth of 
the shadow of the earth is equal to two semi-diame- 
ters of the moon, whereas these are to each other as 
83 to 64. In his sixth proposition, he states the 
apparent diameter of the moon to be one-fifteenth part 
of a sign, or 2° ; whereas we know that it is only about 
half a degree. Again, the distance of the earth from 
the moon being assumed as unity, its distance from 
the sun was said to be 17'107, and the distance of the 
earth from the sun 19081. Such was the astronomical 
knowledge in the time of Aristarchus, who lived about 
264 years before the Christian aera. 

In order of time we puss now to Eratosthenes, who Eratosthe- 
may, perhaps, with more propriety than Autolycus, be °'^^' 
considered as the founder of astronomical science ; ^" ^' ^'^^' 
particidarly if it be true that he placed in the portico 
of Alexandria certain armillary spheres; of which so 
much use was afterwards made, and which, it is said, 
he owed to the munificence of Ptolemy Euergetes, 
who called him to Alexandria, and gave him the 
charge and direction of his library. 

According to the description given of these armil- Ancient ar- 
laries by Ptolemy, they were assemblages of different ^^'^^'"y 
circles ; the principal one of which served as a meri- ^ 
dian ; the equator, the ecliptic, and the two colures, 
constituted an interior assemblage, which turned on 
the poles of the equator. There was another circle, 
which turned on the poles of the ecliptic, and carried 
an index to point out the division at whicli it stopped. 
The instrument of which the above appears to be the 
general construction, was applied to various uses ; 
amongst others, it served to determine the equinoxes, 
after the following manner : — The equator of the in- Determina- 
strument being pointed with great care in the plane '^•o". °^ ^''^ 
of the celestial equator, the observer ascertained, by ci""ioxes. 
watching the moment when neither the upper nor the, 
lower surface was enlightened by the sun ; or rathei, 
which was less liable to error, when the shadow of 
the anterior convex position of the circle completely 
covered the concave part on which it was projected. 
This instant of time was evidently that of the equinox. 
And if this did not happen, although the sun shone, 
two observations were selected, in which the shadow 
was projected on the concave part of the circle in 
opposite directions ; and the mean of the interval 
between these observations was accounted the time of 
the equinox. At this time we find enumerated five 
planets, viz. ^atvwv, (^aeOwv, Uvpocihijp, which appear 
to indicate Jupiter, Saturn, and Mars ; and to which 
were added Venus and Mercury. 

Eratosthenes not only taught the spherical figure of Magnitude 
the earth, but attempted to ascertain its actual cir- of the earths 
cumference, by measuring, as exactly as could be 
done in his time, the length of a certain terrestrial arc. 



ASTRONOMY. 



489 



1 



Archime- 
des. 
B. c. 22 



Astronomy, and then finding the astronomical arc in degrees inter- 
**—>/——' cepted between the zeniths of the two places. The 
segment of the meridian which he fixed upon for this 
purpose, was that between Alexandria and Syene ; the 
measured distance of which was found to be 5,000 
stadia ; and the angle of the shadow upon the scaphia, 
which was observed at Alexandria, was equal to the 
fiftieth part of the circle ; and at Syene there was no 
shadow from this gnomon at noonday of the summer 
solstice ; and that this might be the more accurately 
taken, they dug a deep well, which, being perpendi- 
cular, was completely illuminated at the bottom when 
the sun was on the meridian. The exact quantity 
which this philosopher assigned to the circumference 
of the earth is not known ; at least, different opinions 
have been advanced : some state it at 250,000, and 
others at 252,000 stadia ; the length of this unit of 
measure is also somewhat uncertain. It is, however, 
of small importance, as we may be pretty well con- 
vinced, that by such means as he employed, no very 
accurate conclusion could be expected ; it is sufficient 
that he attempted the solution of the problem in a 
very rational manner, to entitle him to the honour of 
being one of the most celebrated of the Grecian astro- 
nomers. 
Obliquityof Eratosthenes also observed the obliquity of the 
the ecliptic, ecliptic, and made it to consist of -iVc-th of a circum- 
ference, which answers to about 23^ 51' 195''''. This 
observation is commonly stated to have been made in 
the year 230 b. c. 

Archimedes, the justly celebrated geometer of Syra- 
cuse, was contemporary with Eratosthenes ; and 
although most conspicuous as a mechanic and geome- 
trician, the great impulse which he gave to the 
sciences generally, will not admit of our passing him 
over in silence in this history. All that we have of 
this author with reference to astronomy, is found in 
his Arenarius, a work which has been translated into 
most modern languages ; where he undertakes to 
pi-ove, that the numerical denominations which he has 
indicated in his books to Zeuxippes, are more than 
sufficient to express the grains of sand, that would 
compose a globe, not only as large as our earth, but as 
the whole universe. He supposes that the circumference 
of the earth is not more than three million stadia ; 
that the diameter of the earth is greater than that of 
the moon, and less than that of the sun ; that the 
diameter of the sun is 300 times greater than that of 
the moon, and moreover, that the diameter of the 
sun is greater than the side of the inscribed chiliagoUj 
that is greater than -rowj or 21' Z6". 

The manner in which he arrives at his conclusion 
is very interesting, as showing the state of the 
sciences at this time, even in the hands of this gi-eat 
diameter of ™^^ter : — " I have used," says he, " every effort to 
the sun. determine by means of instrumentSj the angle which 
comprehends the sun, and has its summit at the eye 
of the observer ; but this is not easy ; for neither our 
eyes nor our hands, nor any of the means which it is 
possible for us to employ, have the requisite preci- 
sion to obtain this measure. This, however, is not 
the place to enlarge upon such a subject. It will 
suffice to demonstrate that which I have advanced, to 
measure an angle which is not greater than that which 
includes the sun's apparent diameter, and has its 
summit in our eyes j and then to take another angle 



Archime- 
des ascer- 
tains the 



which is not less than that of the sun. and which Historjr. 
equally has its summit in our eyes. Having, there- ^ _,- ^ ^ 
fore, directed a long ruler on a horizontal plane to- 
wards the point of the horizon where the sun ought 
to rise, I place a small cylinder perpendicularly on 
this ruler. When the sun is on the horizon, and we 
look at it without injury, I direct the ruler towards 
the sun, the eye being at one of its extremities, and 
the cylinder is placed between the sun and the eye in 
such a manner, that it entirely conceals the sun from 
view, I then remove the cylinder farther from the 
eye, until the sun begins to be perceived by a thin 
stream of light on each side of the cylinder. Now, if 
the eye perceived the sun from a single point, it would 
suffice to draw from that point tangential lines to the 
two sides of the cylinder. The angle included between 
these lines would be a little less than the apparent 
diameter of the sun ; because there is a ray of light 
on each side. But as our eyes are not a single point, 
I have taken another round body, not less than the 
interval between the two pupils ; and placing this 
body at the point of sight at the end of the ruler, and 
drawing tangents to the two bodies, of which one is 
cylindric, I obtained the angle subtended by the sun's 
(apparent) diameter. Now the body, which is not less 
than the preceding distance (between the pupils), I 
determine thus : I take two equal cylinders, one white 
the other black, and place them before me ; the white 
further off, the other near, so near indeed as to touch 
my face. If these two cylinders are less than the dis- 
tance between the eyes, the nearer cylinder will not 
entirely cover the one that is more remote, and there 
will appear on both sides some white part of that 
remote cylinder. By different trials, we may find 
cylinders of such magnitude, that the one shall com- 
pletely conceal the other : we then have the measure 
of our view (the distance between the pupils), and 
an angle, which is not smaller than that in which the 
sun appears. Now, having applied these angles suc- 
cessively to a quarter of a circle, I have found that 
one of them has less than its 164th part, and the other 
greater than its 200th part. It is therefore evident, 
that the angle which includes the sun, and has its 
summit at our eye, is greater than the 164th part of 
a right angle, and less than the 200th part of a right 
angle." 

By this process, Archimedes found the sun's appa- 
rent diameter to be between 27' and 32' 56". 

It is not a little remarkable, considering the obvious Singular _ 
inaccuracy of the method, that the maximum limit thus accuracy m 
obtained, differs only ^- of a minute from 32' 3 5"- 6, "^-'^ ''^^''"■• 
which is the largest angle actually subtended by the 
sun's diameter, and which is observed about the time 
of the winter solstice, Avhen the sun is nearest to the 
earth. But this quotation from the Arenarius is 
extremely curious also on other accounts. We may 
learn from it, first, that Archimedes, with all his 
fecundity of genius, and with all the variety of his 
inventions, had no means of diminishing the effect of 
the sun's rays upon his eyes, and therefore performed 
this interesting experiment when the sun was in the 
horizon, that the optic organ might sustain its light 
without inconvenience. It also proves to us, that 
there was not then any instrument known to Archi- 
medes, which he thought capable of giving the 
diameter of the sun, to within four or six minutes : 



i 



490 



ASTRONOMY. 



Astronomy 



Kipparclius 
B. c. 135. 

Finds the 
length of 
the year. 



Introduc- 
tion of tri- 
gonometry 
by chords. 



Establishes 
the theory 
of the sun's 
motion, 

and the first 
lunar in- 
equality. 



Hour of the 
night found 
by the stars. 



since he found it necessary to devise means at which 
he stopped, after an attempt not very satisfactory. 
We see, further, that he carried his angles, or their 
cliords, over a quarter of a circle ; but he does not say 
expressly that his arc had been divided ; to render 
his language accurately, it is simply requisite to say, 
ha-^'ing- carried one of the chords 200 times over upon 
the arc, he found it exhausted ; and that the other 
chords could only be applied 164 times upon the 
quadrant. 

We see, also, that Archimedes had not the means of 
computing the angle at the vertex" of an isosceles tri- 
angle, of which he knew the base and the two equal 
sides. He was obliged to recur to a graphical opera- 
tion as uncertain as the observation itself. Thus he 
was entirely ignorant even of rectilinear trigonometry, 
and he had not any notion of computing the chords of 
circidar arcs. 

We come now to the great father of true astronomy, 
Hipparchus ; but our limits will not admit of our 
entering very deeply into his discoveries and improve- 
ments. One of his first cares was to rectify the length 
of the year, which before his time we have seen had 
been made to consist of 365 days and 6 hours. By 
comparing one of his own observations at the summer 
solstice with a similar observation made 145 years 
before by Aristarchus, he shortened the year about 
7 minutes ; making it to consist of 365 days, 5 hours, 
53 minutes ; which, however, was not sufficient : but 
the cause of the mistake is said to have rested prin- 
cipally with Aristarchus, and not with Hipparchus ; 
for the obsen-ations of the latter, compared with 
those of modern times, give 365 days, 5 hours, 48 
min, 49iJ- sec. for the duration of the year ; a result, 
which exceeds the tmth very little more than a second. 
It is to be observed, however, that this is no very 
exact criterion, unless the same be compared with 
the observation of the more ancient observer ; for 
supposing all the error on the side of Hipparchus, it 
is more divided by comparing it with others at the 
distance of 19 or 20 centuries, than in comparing it 
with one, where the distance of time is only 145 
years. 

One of the greatest benefits, which astronomy 
derived from this philosopher was his enunciation and 
demonstration of the method of computing triangles, 
whether jjlane or spherical. He constructed a table 
of chords, which he applied nearly in the same man- 
ner as we now do our tables of sines. As an ob- 
server, however, he rendered great service to tho 
doctrine of astronomy, having made much more 
numerous observations than any of his predecessors, 
and upon far more accurate principles. He esta- 
blished the theory of the sun's motion in such a 
manner, that Ptolemy 130 years afterwards, found no 
essential alteration requisite ; he determined also the 
first lunar inequality, and gave to the motions of the 
moon those of the apogee and of its nodes, which 
Ptolemy afterwards very slightly modified. Hippar- 
clius also prepared the way for the discovery of the 
second lunar inequality, and from his observation it 
was, that the fact of the precession of the equinoxes 
was first inferred. He employed the transit of the 
stars over the meridian to find the hour of the night, 
and invented the planisphere, or the means of repre- 
senting the concave sphere of the stars, on a plane. 



and thence deduced the solution of problems in spherl- Historyi 
cal astronomy, with considerable exactness and facility. *^— — >/-^p' 
To him also we owe the happy idea of making the 
position of towns and cities, as we do those of the stars, 
by circles drawn through the poles perpendicularly to 
the equator ; that is, by latitudes and by circles 
parallel to the equator, corresponding to our longi- 
tudes. From his projection it is, that our maps and 
nautical charts are now principally constructed; and 
his rules for the computation of eclipses were long the 
only ones employed for determining the differences of 
meridian. 

Another most important work of Hipparchus, was Catalogue 
his formation of a catalogue of the stars. The appear- of the stars. 
Jmce of a new star in his time, caused him to form the 
grand project of enabling future astronomers to ascer- 
tain, whether the general picture of the heavens were 
always the same. This he aimed to effect, by attempt- 
ing the actual enumeration of the stars. The magni- 
tude and difficulty of the undertaking did not deter 
this indefatigable astronomer ; he prepared and 
arranged an extensive catalogue of the fixed stars, 
which subsequently served as the basis of that of Pto- 
lemy. So great, indeed, is the merit of this prince of 
Grecian astronomy, that the enthusiastic language in 
which Pliny speaks of him in his Hist. Nat. (lib. ii. 
cap. 26.) may rather be admired than censured. 

After Hipparchus, we meet witli no astronomer of Ptolemy, 
eminence amongst the Greeks till the time of Ptolemy, a. d, 120. 
who flourished between the years 125 and 140 of the 
Christian asra ; which, therefore, includes a space of 
nearly three hundred years. There were, however, 
some astronomical writers, both Greeks and E.oman,'v.«^*'' 
in the course of this time, whom it may not be amiss 
to enumerate, although the little progress that the 
science made in their hands will exempt us from the 
necessity of entering minutely into an analysis of their 
several works : these Avere, Geminus, who lived 
about 70 years b. c, whose book is entitled Introduc- 
tion to the Phenomena ; Achilles Tatius, of about the 
same period ; Cleomedes, who lived in the time of 
Augustus ; Tlieodosius, Blenalaus, and H\'psicles, who 
are supposed to have written about the year 50 b. c. ; 
INIanilius, Strabo, Posidonius, and Cicero, who were 
about half a century later ; after which, we meet 
with no one to whom it is at all necessary even to 
refer, till we come to Ptolemy, who was born in the 
year of Christ 70 ; and who made, as we have stated 
above, most of his observations between the years 125 
and 140 of our sera. 

Ptolemy has rendered all succeeding astronomers Various la- 
indebted to him, both for his own observations, which ^oms of 
were very numerous, and his construction of various P'o'^my. 
tables ; but most of all for the important collection 
which he made of all astronomical knowledge prior 
to his time, and which he entitled, or the yVra-bs after 
him, the Almagest, or Great Collection. Of his own 
labours, Ave may mention his theory and calculation of 
tables of the planets, and his determination, with a 
precision little to be expected in his time, of the ratio 
of their epicycles to their mean distances ; that is to 
say in other terms, the ratio of their mean distartces 
to the distance of the earth from the sun. This theory, 
imperfect as it Avas, was adopted and generally ad- 
mitted, for the space of fourteen centuries ; during 
which time, it was transmitted to the Arabs, the Per- 



ASTRONOMY. 



491 



Astronomy, sians, and the Indians, and with whom it is still held 

\— -y— ~^ sacred. The equi-distant centres of the earth, from 

the excentric and the equant, an hypothesis of Ptolemy, 

led, in all probability, Kepler to the idea of an ellipse 

and its foci. Ptolemy thiis preparing the way for 

Kepler, as the laws of the latter may be considered 

as the precursors of the theory of Newton. 

Sines intro- To this celebrated Grecian we also owe the substi- 

duced into tution of the sines of arcs instead of their chords; as 

trigonome- ^igQ ^he first enumeration of some important theo- 

^'^' rems in trigonometry. 

Ptolemy's Ptolemy was the author of that system of astro- 
arguments nomy which still bears his name ; or if he did not 
?°P''°'''!;.*'*^ entirely invent it, (as there is great reason to sup- 
oTt^eeartt P*^^^ ^^ *^"^ not,) he enforced it by such arguments as 
led to its establishment ; and it was afterwards ren- 
dered sacred through the stupid bigotry and intol- 
erance of the Romish church. He endeavours to prove 
the absolute immobility of the earth, by observing, 
''If the earth had a motion of translation common to 
other heavy bodies, it would, in consequence of its 
superior mass, precede them in space, and pass even 
beyond the bounds of the heavens, leaving all the 
animals and other bodies without any support but air ; 
which are consequences to the last degree ridiculous, 
and absurd." In the same place he adds, " Some 
persons pretend, that there is nothing to prevent us 
from supposing that the heavens remain immovable^ 
while the earth turns on its own axis from west to 
east, making this revolution in a day nearly ; or, that 
if the heavens and the earth both turn, it is in a 
ratio corresponding with the relations we have ob- 
• served between them. It is true, that as to the stars 

themselves, and considering only their phenomena, 
there is nothing to prevent us, for the sake of simpli- 
city, from making such a supposition. But these 
peopls are not aware how ridiculous their opinion is, 
when considered with reference to events which take 
^ place about us ; for if we concede to them that the 

lightest bodies, consisting of parts the most subtle, 
are not possessed of levity, (which is contrary to 
nature,) or that they move not differently from bodies 
of a contrary kind, (although we daily witness the 
reverse) ; or, if we concede to them that the most 
compact and heaviest bodies possess a rapid and con- 
stant motion of their own (while, it is well known, 
that they yield only with difficulty to the impulses 
we give to them), still, they would be obliged to 
acknowledge, that the earth, iDy its revolution, would 
have a motion more rapid than any of those bodies 
which encompass it, in consequence of the great cir- 
cuit through which it must pass in so short a period ; 
wherefore such bodies as are not supported on it, 
would always appear to possess a motion contrary to 
itself; .and neither clouds, nor any projected bodies, 
nor birds in flight, would ever appear to move towards 
the east ; since the earth, always preceding them in 
this direction, would anticipate them in their motion ; 
and every thing, except the earth itself, would con- 
stantly appear to be retiring towards the west." 

If we did not feel convinced that, in certain cases, 
even the errors and false reasoning of such a man as 
Ptolemy, possess a greater interest than the more 
correct and refined arguments of minor philosophers, 
•we should certainly not have laid before our readers 
this extract from the introduction to the Almagest ; 



but considering it as the defence of an hypothesis, Historj'. 
which maintained its ascendancy for fourteen centuries "^^ i.-s^^,-.»^ 
amongst all nations, and which is still held sacred 
throughout every part of Asia, it is impossible to 
divest it of its interest and importance. 

The other part of this great work is more worthy Analysis of 
of the talents of its author, and is more deserving of '^'^ ^^^ma- '• 
our attention ; but the limits of this article will nof^^*'" 
admit of our giving more than a very concise abstract 
of its contents. The first book, beside what we have 
hitherto mentioned, exhibits a highly interesting spe- 
cimen of the ancient trigonometry ; and the method 
of computing the chords of arcs, which, in fact, in- 
volves our fundamental theorems of trigonometry, 
though expressed in a manner totally different. 

Ptolemy first shows, how to find the sides of a Theorems 
pentagon, decagon, hexagon, square and equilateral '° t"gono- 
triangle, inscribed in a circle, which he exhibits in ™^ ^^' 
parts of the diameter, this being supposed divided into 
120. He next demonstrates a theorem equivalent to 
our expression sin (a—b) = sin a cos i — sin b cos a ; 
by means of which he finds the chords of the difference 
of any two arcs, whose chords are known. He then 
finds the chord of any half arc, that of the whole arc 
being given, and then demonstrates what is equivalent 
to our formula for the sine of two arcs ; that is, sin. 
(a-\-b) = sin a cos b -)- sin b cos a; and by means 
of this he computes the chord to every half degree of 
the semicircle. These theorems it may be said belong 
rather to the history of trigonometry than to that of 
astronomy ; but we trust that the obvious dependence 
of the latter science upon the former, will be found to 
justify us in introducing them to the reader in this 
place. 

We are next presented with a table of climates Climates, 
nearly equivalent to our nonagesimal tables, and it is 
not a little singular, that amongst them, we find none 
appertaining to the latitude of Alexandria ; because, 
without such an auxiliary, Ptolemy must have con- 
tented himself with interpolations, which were not 
only difficult to make, but attended at the same time 
with great inaccuracy ; a circumstance from which it 
has been concluded, that Ptolemy himself made few 
observations, or that he was not very particular con- 
cerning the accuracy of his calculations. The exami- 
nation of this question would carry us too far out of 
our track to admit of our entering upon it in this place ; 
but the reader may see it developed in all requisite 
detail, in the learned History of Astronomy, lately pub- 
lished by Delambre. 

Having passed over the above preliminary details. Length of 
the author treats of the length of the year, the motion ^® y^^""' 
of the sun, the mean and apparent anomaly, &c. &c. 
The length of the year, according to the sexagesimal 
notation, he makes 365d. 14' 48", which answers to 
365d. 5h. SS' l^'' ; the diurnal motion of the sun is 
stated to be O^ 59' 8''7''^ 13'" 12" 31"', and the horary 
motion 2' 27" 50'" 43'" 3" 1"', To this is also added 
two tables, one of the mean motion of the sun, 
and the other of the solar anomaly. The fourth book 
of the Almagest is employed in treating of the motion 
of the moon, being prefaced by a few remarks respect- 
ing the observations which are most useful for that 
purpose : he then gives an abstract of all the lunar 
motions, with a table of them ; in the first of which 
the motion is exhibited for periods of eighteen years ; 



&c. 



492 



ASTRONOMY. 



Lunar mo 
tion. 



Particular 
deductions 



Astronomy, in the second for years and hours ; and in the third 
^— -v-™*' for Egyptian months and days. Four other columns 
of the same table present the number of degrees which 
belong to each of the times indicated in the first 
column ; viz. the second, the longitude j the third, 
the anomaly ; the fourth, the latitude ; and the fifth, 
the elongation. 

The author next treats of various subjects connected 
with the lunar motion ; as, for instance, its general 
anomaly ; its eccentricity ; the lunar parallax ; the 
construction of instruments for observing the parallax ; 
the distance of the moon from the earth, which he 
states at 38-4-^- terrestrial radii, when in the quadra- 
tures j the apparent diameters of the sun and moon ; 
the distance of the sun from the earth, which is stated 
at 1210 radii of the latter ; and the relative magni- 
tudes of the sun, moon, and earth. The diameters 
of these are stated to be to each other, as the numbers 
18'8, 1, and 3-^ ; also their masses as 66444-, 1 and 39^^. 
The next book is entirely occupied with the doc- 
trine of eclipses of the sun and the moon ; the deter- 
mination of their limits and durations ; tables of 
conjunctions ; and methods of computation and 
construction, &c. 

We cannot extend the analysis of this important 
work to a greater length ; but must content ourselves 
o emy. ^j^jj j^ fg^y remarks relative to some of the deductions 
to which we have referred. We have seen that Pto- 
lemy made the length of the year to be more than 365 
days, 5h. 55m., which is about 6 minutes longer than 
it really is ; but considering that the observations be- 
fore his time, with the exception of those of Hippar- 
chus, were very imperfect ; and that the distance of 
time between these two celebrated astronomers, was 
not sufficient to determine such a question, with 
the means they possessed, to the greatest nicety, we 
may rather admire the near approximation to the 
truth, than be astonished at the diiference between his 
result and that deduced from numerous and long con- 
tinued observations. 

His researches on the theory of the sun and moon 
were however attended with better success. Hippar- 
chus had shown that these two bodies were not placed 
in the centre of their orbits ; and Ptolemy demon- 
strated tlie same truths by new observations. He 
moreover made another important discovery, which 
belongs exclusively to him, except so far as relates to 
the observations of Hipparchus, by a comparison of 
which with his own, his conclusion was deduced, — 
we allude here to the second lunar inequality, at pre- 
sent distinguished by the term evection. It is known, 
generally, that the velocity of the moon in its orbit, 
is not always the same, and that it augments or dimi- 
nishes, as the diameter of this satellite appears to 
increase or decrease ; we know, also, that it is great- 
est and least at the extremities of the line of the 
apsides of the lunar orbit. Ptolemy observed that 
from one revolution to another ; the absolute quan- 
tities of these two extreme velocities varied, and that 
the more distant the sun was from the line of the 
apsides of the moon, the more the difference between 
these two velocities augmented ; vv'hence he concluded 
that the first inequality of the moon, which depends on 
the eccentricity of its orbit, is itself subject to an annual 
inequality, depending on the position of the line of the 
apsides of the lunar orbit with regard to the sun. 



The evec- 
tion disco- 
vered 



When we consider Ptolemy's system of astronomy. History, 
as founded upon a false hypothesis, the complication ^— v— ^ 
of his various epicycles, in order to account for the 
several phenomena of the heavenly bodies ; and the 
rude state of the ancient astronomy, it is impossible 
to withhold our admiration of the persevering industry 
and penetrating genhis of this justly celebrated philo- 
sopher ; who, with such means, was enabled to discover 
an irregularity which would seem to require the 
most delicate and refined aid of modern mechanics 
to be rendered perceptible. 

The work of this author to which we have hitherto 
confined our remarks, is the Almagest ,-* but Ptolemy also 
composed other treatises ; which,ifnot equal to theabove 
in importance, are still such as to be highly honourable 
to his memory and talents, particularly his geography. 

This work, although imperfect as to its detail, is Ptolemy's 
notwithstanding founded upon correct principles ; the geography, 
places being marked by their latitude and longitude 
agreeably to the method of Hipparchus. As to the in- " 
accuracies of their position, although they cannot be 
denied, they will readily be pardoned, when we consider 
that he had for the determination of the situation of 
cities and places of which he speaks, only a small number 
of observations subject to considerable errors ; and the 
mere report of travellers, whose observations we may 
readily grant were still more erroneous than those of his 
own. It requires many years to give great perfection to 
geography : even in the present time, when observations 
with accurate instruments have been made in every part 
of the globe, we are still finding corrections necessary ; 
a remarkable instance of which seems to have occurred 
lately (1818) to Captain Ross, in his voyage into 
Baffin's Bay, where he is said to have found some 
parts of the land laid down nearly a degree and a half 
out of their proper places. Many other minor pieces 
on astronomy and optics are also attributed to this 
author ; but we have already extended our accounts of 
his works to a greater length than we had intended, 
and must now therefore pass on to his successors. 

After the time of Ptolemy we find no Greek authors Greeks 
of eminence, although Ave have some few writers on posterior to 
this subject. The science of astronomy had now ^'"^^'"y- 
obviously passed its zenith, and began rapidly to 
decline. The Alexandrian school, it is true, still sub- 
sisted ; but during the long period of 500 years, all 
that can be said is, that the taste for, and the tradition 
of the science was preserved, by various commentators 
on Hipparchus and Ptolemy ; of whom the most dis- 
tinguislied were Theon and the unfortunate Hypatia, 
his daughter. The latter is said to have herself 
computed certain astronomical tables, which are lost. 

We now arrive at that period, so fatal to the Grecian Destruction 
sciences. These had for a long time taken refuge in ofthe Alex- 
the school of Alexandria ; where, destitute of support ^"''"^i 

* The first printed edition of this celebrated performance, was 
a Latin translation from the Arabic version of Cremoneus ; which, 
however, abounds so much in the idiom of that languag^e, as to 
render it nearly unintelligible, without a constant reference to the 
Greek text. This was published at Venice in 1515 ; and in 1538 
the collection appeared in its original language, under the super- 
intendence of Simon Grynaens, at Basil, togetlier with the eleven 
books of the Commentaries of Tlieon. The Greek text was again 
republished at the same place, with a Latin version, in 1541 ; and 
again, with all the works of Ptolemy, in 1551 ; and lastly, a 
splendid French edition with the Greek text, by M. Halma, ia 
three beautiful volumes, royal quarto, Paris, 1813. 



ASTRONOMY. 



493 



Aatronomy. and encouragement, they could not fall to degenerate. 

^-•->r"~^ Still, however, they preserved, as we have said above, 
at least by tradition or imitation, some resemblance of 
the original; but about the middle of the seventh 
century, a tremendous storm arose which threatened 
their total destruction. Filled with all the enthusiasm 
a military government is calculated to inspire, the suc- 
cessor of Mahomet ravaged that vast extent of country, 
which stretches from the east to the southern confines 
of Europe. All the cultivators of the arts and sciences 
who had from every nation assembled at Alexandria, 
were driven away with ignominy : some fell beneath 
the swords of their conquerors, while others fled into 
remote countries, to drag out the remainder of their 
lives in obscurity and distress. The places and the 
instruments which had been so useful in making an 
immense number of astronomical observations, were 
involved with the records of them, in one common 
ruin. The entire library, containing the works of so 
many eminent authors, which was the general depo- 
sitory of all human knowledge, was devoted to the 
devouring flames, by the Arabs ; the caliph Omar 
obsersang, " that if they agreed with the Koran, they 
were useless ; and if they did not they ought to be 
destroyed :" a sentiment worthy of such a leader, and 
of the cause in which he was engaged. In the midst 
of this conflagration, the sun of Grecian science, 
which had long been declining from its meridian, 
finally set ; never perhaps again to rise in those re- 
gions once so celebrated for the cultivation of every 
art and science that does honour to the human mind. 

Astronomy of the Chinese and Indians. 
Astronomy If we were to adopt the opinions of some authors 
of the Chi- ■who have written on the subject of the Chinese astro- 
°*^*' nomical knowledge, we should have now to com- 

mence at a much earlier period than we did in giving 
our account of this science amongst the Greeks ; as 
it is stated that the former possess records of eclipses 
and other celestial phenomena, so far back as the 
year 2159 b.c, and that even in the year 2857 b. c. 
the study of astronomy and the desire of propagating 
a knowledge of that science amongst his people, were 
objects of great moment with the emperor Ion Hi ; 
such at least is the doctrine supported in the Histoire 
Generate de la Chine, ou Annates de cet Empire, trans- 
lated into French from Tong-Kien-Kang-Mou, by 
the Pere De-Mailla, a French Jesuit, one of the mis- 
sionaries to Pekin. 

We cannot attempt to enter here upon a refutation 
of the ideas supported in this work, relative to the 
antiquity of the Chinese astronomy ; it will perhaps 
be sufficient to observe, that of 460 eclipses reported 
to have been predicted and recorded in the Chinese 
annals, the first is dated 2159 b. c, and the second, 
776 B. c, leaving a great blank of 1383 years, during 
which no such phenomenon is noticed. That from the 
latter date to the year 1699 of our aera, they run on 
in pretty regular succession ; but that of this number^, 
the Pere Gaubil, who was at the labour of com- 
puting them, found only twelve which answered to 
the year, month, and day stated in the annals ; and 
that of these twelve, only one of them was anterior to 
The ami- the time of Ptolemy, and even this one is doubtful, 
quityofit It appears then that very little credit is to be given 



perhaps the following abstract, which Delambre has History, 
made from the annals above referred to, will give the ^— "V"* 
reader a better idea of the state of astronomy amongst 
this singular people, and place their pretensions in a 
more tangible form than any thing we can advance 
respecting the improbability of the notions advanced 
by Mailla. 

In the year 687 b. c. we find recorded a night with- 
out stars, and without clouds ; and that towards mid- 
night, there fell a shower of stars, which vanished 
before they approached the earth. 

14 1 B. c. The sun and moon appeared of a deep red 
colour, which produced great alarm among the 
people. 

74 B. c. There appeared a star as big as the moon, 
followed by many other stars of the ordinary mag- 
nitude. 

38 B. c. A shower of stones as big as nuts. 

S8 A. D. Another shower of stars. 

321. Spots in the sun visible to the naked eye. 

522. The astronomy of Hiuen-Chi-Ly was replaced 
by the astronomy of Tching-Kouange-Ly. (We do not 
understand these to be the names of astronomers but 
of systems.) In the year 892, another change is 
recorded ; and again in 956. 

In 949, in the fourth moon, there appeared a star 
in the mid-day, which was regarded as such a dread- 
ful omen, that the people were forbidden to look 
at it ; and many were put to death for disregarding 
the injunction. 

These facts alone, independent of the superstitious 
fears and ceremonies, which even to this day are 
observed during the time of an eclipse, would alone 
give us a sufficient contempt for the astronomy 
of the Chinese ; and lead us to reject as mere 
fables their pretensions to ancient observations. 
All that we can concede to them, and to the Indians, 
whose claims rest upon nearly the same grounds, is 
what we have already attributed to the Chaldeans, 
viz. that they had become, very early, observers 
of the motions and phenomena of the heavenly 
bodies; that they registered certain events, and 
thence were able to discover periods at which these 
phenomena would return again ; sufficiently approxi- 
mate to admit of their predicting an eclipse or occult- 
ation, within certain limits ; but frequently, their 
prediction has been belied by the non-appearance of 
the expected phenomenon, while others have happened 
that were not foretold ; which omissions, as well as 
a false prediction, have cost some few unfortunate 
astronomers the forfeiture of their heads : of which a 
particular instance is recorded in the case of Hi and Ho. 

Upon the whole, therefore, we may conclude, that 
however ancient may be the rude observations of the 
Chinese and Indians, they possessed no science, pro- 
perly so called, but wliat they obtained from the 
Greeks, through the medium of the Arabs ; which 
people, after deriving it from the former source, 
carried it to Persia, whence it was transmitted to 
India and China. Such at least is the conclusion 
drawn by M. Delambre from a dispassionate exami- 
nation of all the claims of these nations. We are 
aware that this notion is totally at variance with that 
of BaiUy, who has also examined the case in point 
with great labour and attention, but certainly not 
without great enthusiasm and prejudice. 
3 s 



494 



ASTRONOMY. 



Astronomy. Astronomy of the Arabs. 

V— -s,^—^^ In our last mention of this people, we saw them 
Astronomy acting the part of the most savage barbarians, burn- 
of the Arabs ing and destroying- every thing, the most distantly 
connected with scientific research ; we have now to 
exhibit them in a more honourable and dignified 
point of view. We stated, in the passage referred to^ 
that some of the philosophers of Alexandria, escaped 
the \engeance of their barbarous conquerors, and 
these of course carried with them some remnant of 
that general learning, for which the school was so 
deservedly celebrated. Still, however, destitute of 
books, of instruments, and probably also of the 
means of subsistence without inanual labour, very 
little farther knowledge could be accumulated, and 
still less propagated ; so that in a few years, every 
species of knowledge connected with astronomy and 
mathematics, must have become extinct, had not the 
Arabians themselves within less than two centuries of 
the dreadful conflagration of the Alexandrian library, 
become the admirers and supporters of those very 
sciences they had before so nearly annihilated. They 
studied the works of the Greek authors which had 
escaped the general wreck, with great assiduity ; and 
if they added little to the stock of knowledge these 
works contained, they became sufficient masters of 
many of the subjects to enable them to comment upon 
them, and to set a due estimation upon these valuable 
relics of ancient science. 

The destruction of the Alexandrian school occurred 
in the year 640 ; and it is about a century after, 
before we find any author worthy of particular no- 
tice amongst the Arabs ; this, therefore, brings us 
to the middle of the eighth century ; and from Ptolemy 
to this date there had passed away at least six hun- 
dred years, during which time the science had rather 
Almansor. retrograded than advanced. The caliph Almansor, 
A.D. 754. A. D. 754, is the first to claim our attention ; but rather, 
perhaps, for the impulse, which, as a philosophical 
prince, he gave to the science amongst his people, 
than for any actual improvements which he had per- 
sonally made. This impulse was, however, so great, 
that most of his successors seem to have thought it 
their duty to support and to study the diiferent sci- 
Haroun. ences, particularly astronomy. Haroun, the grand- 
A.D 786 ^"'^ °^ Almansor, is particularly noticed as foUomng 
in the steps of his great predecessor ; and one of his 
Almamon. sons, Almamon, pursued the same path with still 
A.D. 813. greater enthusiasm. He caused to be translated all 
the Greek works that he could procure ; and in par- 
Translate ticular the Almagest of Ptolemy. He is even said to 
the Alma- have made the delivery of certain manuscripts depo- 
gest. sited at Constantinople, one of the conditions of the 

peace which he concluded with the Greek emperor 
Michael HI. He himself made numerous observa- 
tions, and employed and instructed others to supply 
his place, when public business prevented him from his 
favourite pursuit. He ordered the obliquity of the 
ecliptic to be observed at Bagdad and at Dumas ; 
whence it was found to be 23" 3.5', which is less than 
some preceding observations had indicated. 
Measures a Another important operation perforixied under the 
degiee of orders of Almamon, was the measure of a degree of 
Jatitade. the terrestrial meridian ; but the unit of the Arabic 
measure in which it is expressed, is too uncertain for 
us to attempt to form from the reported result any 



decisive conclusion ; nor are we to expect that any History. 
very great accuracy could be expected, seeing the ». ,^ -J^j 
great discrepancy between some modern measures 
made with the assistance of the most perfect instru- 
ments. Almamon also directed certain of his philo- 
sophers to compose a work for the purpose of facili- 
tating the study of astronomy amongst his people, 
entitled, according to the Latin translation, Astronomia 
elaborata a compluribus D. D.jussu regis Maimon. which 
is still preserved in many libraries. 

In the reign of this prince, there were many other Alfra?anus 
celebrated Arabian astronomers, particularly Alfra- ^ p qk^q ' 
ganus, Thebit-Ibn-Chora, and Albatenius. The 
former composed a work, many editions of which 
have been made since the invention of printing, be- 
sides some other works more or less connected with 
this science. 

Thebit was an annalyst, a geometer, and astronomer. Tliebit. 
He observed the obliquity of the ecliptic and reduced a.d. 860. 
it to 23° 33' 30". He also determined the length of 
the year, very nearly the same as it is now established 
by modern observations. 

Albatenius was one of the greatest promoters of Albatenius. 
Arabian astronomy. His numerous observations and a.d. 879. 
important knowledge in all the sciences of his time, 
were the cause of his being surnamed the Ptolemy of 
the Arabs ; an honour by no means ill merited. By 
a comparison of many of his own observations with 
those of Ptolemy and others, he coi-rected the determi- 
nation of the latter respecting the motion of the stars 
in longitude, stating it to be one degree in 70 years 
instead of 100 years : modern observations make it 
one degree in 72 years. He determined very exactly 
the eccentricity of the ecliptic, and corrected the 
length of the year, making it consist of 365 days 5 
hours 46 minutes 24 seconds, whiclr is about 2 mi- 
nutes too short, but 4 minutes nearer the truth than 
had been given by Ptolemy. He also discovered the 
motion .of the apogee ; and rectified the theories of 
Ptolemy respecting the motion of the planets , and 
formed new tables of them. 

The works of this author have been collected, and 
published in 'two volumes 4to., under the title of De 
scientia stellarum, of which there are two editions, one 
in 1537, and the other in 1646. 

Montucla, in his valuable history of mathematics, 
enumerates a long list of Arabian astronomers which 
followed Albatenius ; but we meet with none de- 
serving of particular notice till we arrive at £bn 
lounis, who wrote in the year 1004, and even he is 
rather celebrated for his having collected and embo- 
died the knowledge of his time, than for his dis- 
coveries, although he made numerous observations. 
The work of this author is still extant, a concise no- 
tice of which Delambre has given in the Mem. de 
rinstitut, vol. 2. p. 5, where we learn, that it contains 
28 observations of eclipses of the sun and moon, made 
between the years 829 and 1004 ; seven observations 
on the equinoxes ; one on the obliquity of the eclip- 
tic : and some others highly important in the deter- 
mination of certain data, particularly as regards the 
acceleration of the moon. 

Let us now turn our attention to Spain, where the 
Arabs, who had long been masters of that country, 
pursued the sciences with the same ardour as in the 
east. The most distinguished, however, of the astro- 



ASTRONOMY. 



495 



Astronomy, nomers in this country were Arsachel and Alhazen ; 
t_^ ^1 the former of whom is celebrated for having added 
Arsachel. greater acciiracy to the theoiy of the smi, by employ- 
A,D, 1020, ing a principle different to that of Ptolemy and Hip- 
parchus, and susceptible of more accuracy. He made 
some fortunate changes in the dimensions of the 
solar orbit, and discovered certain inequalities in the 
sun's motion, which have since been confirmed by 
the Newtonian theory of gravitation. 
Alhazen. Alhazen is also esteemeil a philosopher and astro- 

nomer of high reputation ; he is said to have first 
discovered the laws of refraction, and the effect of it 
^in astronomical observations. He explained the phe- 
nomenon of the horizontal moon, and indicated the 
true cause of the crepuscula in the morning and even- 
ing) beside various other minor discoveries highly 
honourable to his memory. 

From this time the science of the Arabians seems to 
have begun to decline ; we meet with very little after 
this period deserving of particular notice ; a general 
shade appears to have been cast over every species of 
human knowledge, and nearly four hundred years are 
again lost in darkness and obscurity. We then find 
the Greeks making some feeble efforts to re-establish 
astronomy in its original empire, where some faint 
glimmerings of the genius which animated Archime- 
des, Hipparchus, and Ptolemy, once more began to 
discover itself j but which, alas ! like the lustre of a 
passing meteor, was soon extinguished, and darkness 
and barbarity once more assumed their reign. 

Astronomy of modern Europe. 
Copernicus We may without impropriety refer the revival of 
died 1543, modern astronomy to the time of Copernicus, although 
he was preceded by some others, who prevented all 
traces of the Grecian and Arabic science from being 
lost and forgotten, by their reading and studying such 
works as had been preserved, during what are com- 
monly denominated the dark ages. Copernicus was 
born at Thorn, in Poland, in the year 1473, but he did 
not commence his studies till about the year 1507 ; 
when after having well " fathomed every depth and 
shoal" of the ancient doctrine of astronomy ; made 
numerous observations, and various comparisons ; he 
became at first a convert, and afterwards the most 
strenuous advocate of a system of astronomy, com- 
monly attributed to Pythagoras, and which we have 
seen Ptolemy using so many ingenious but false argu- 
ments to refute. 
System of According to Copernicus, the sun is placed in the 
Copernicus centre of the planetary world, about which the seve- 
ral bodies of our system revolve from west to east ; 
^dz. 1st, Mercury, 2d, Venus, 3d, the Earth, 4th, 
Mars, 5th, Jupiter, and 6th, Saturn ; the m.oon re- 
volves about the earth in the same direction, while 
the latter body itself is carried in its orbit round the 
sun. In the next place, he taught that the earth turns 
on its own axis from west to east, in a little less 
than 24 hours, and that this axis is always preserved 
parallel to itself, making an angle of about 234-° with 
the ecliptic. 

The orbits of the several planets he supposed to be 
circular ; but he did not make the sun their common 
centre. We have seen that what was anciently called 
the solar orbit had been long known to be eccentric, 
as well as those of the planets ; and to account for 



the phenomena produced by these eccentricities, Co- History, 
pernicus rendered them still greater, by giving to each ^ _ _> 
a different centre, and to the sun such a position with 
regard to them all, as with the addition of certain 
epicycles, best agreed with the appearances already 
observed. This part of the Copernican system is not 
often Avell illustrated in our elementary works on 
astronomy, where it is generally asserted, that the 
sun was placed in the common centre, and the several 
planetary orbit-s were circles concentric with it ; by 
which means, the discoveries of Kepler are rendered 
more astonishing than they actually are ; for he had 
at least this much to proceed upon ; too little, it is 
true, for any man possessed of less genius and perse- 
verance than himself. This is by no means the only 
service which Copernicus bestowed upon astronomy 
and trigonometry, but it is the principal one, and 
that which has added most to the celebrity of his 
name ; we shall therefore not stop to report his other 
discoveries and improvements, as we shall find 
numerous important points to refer to before we 
conclude this sketch, already considerably extended. 
The work containing his new doctrine was composed 
in the year 1530 ; but it was not printed till the year 
1543 ; the author having, it is said, received the last 
sheet a few hours before he expired. 

Copernicus was followed by a great number of ex- 
cellent astronomers, some of whom were firm sup- 
porters of his system j others endeavoured to refute 
it, as Ptolemy had formerly done a similar doctrine ; 
while some few who saw its beauties and advantages, 
but who by giving too literal a signification to some 
scriptural passages, wished to modify it so as to retain 
as many as possible of its advantages, while the system 
should still be such as to correspond with the pas- 
sages in question. 

Of this number was Tycho Brache, a noble Dane, Tycho 
one of the greatest observers perhaps, if we except Brache died 
Kepler, that ever lived. His system consisted in depriv- 1601. 
ing the earth of its orbicular and diurnal motion ; he 
places the earth in the centre, and made the moon and 
sun revolve about it, agreeably to the doctrine of 
Ptolemy ; but he made the sun the centre of the other His system, 
planets, which, therefore, he supposed to revolve 
with the former about the earth. By this means, the 
different motions and phases of the planets may be 
reconciled, the latter of which could not be by the 
Ptolemaic system ; and he was not obliged to retain 
the epicycles, in order to account for their retrograde 
and stationary appearances. This theory was ex- 
tremely complicated, and did not long survive its coVeries'^of 
author. Many of his other labours were attended Tycho 
with much more important consequences ; particularly 
his discovery of the variation and annual equation of 
the moon ; the greater and less inclination of the lunar 
orbit ; the correction for refraction in astronomical 
observations ; his astronomy of comets ; his account 
of the appearance and disappearance of a great star 
which happened in his time : his reformation of the 
calendar, and some other subjects which might be 
enumerated : these have contributed most to esta- 
blish his name as a great astronomer, and will not 
fail to hand it down to the latest posterity. 

Kepler was about twenty years younger than Tycho, Kepler died 
but by no means inferior to him in genius and perse- 1631. 
verance ; the latter quality is proved by the numerous 
3 s2 



496 



ASTRONOMY. 



Astronomy, observations that he made on all the planets, particu- 
larly on Mars ; and the former from the memorable 
consequences which he drew from them. Kepler first 
determined the line of the apsides by a method inde- 
pendent of the form of the orbit of Mars, and ascer- 
tained the ratio of the aphelion and perihelion distances ; 
the former he found to be to the latter, as 166,780 to 
138j50O ; or calling the distance of the earth from the 
sun 100,000 ; the above numbers will express the 
actual distances. Hence the mean distance of Mars 
was 152,640, and the eccentricity of its orbit 14,140. 
He then determined, in like manner, three other 
distances, and found them to be 147,750 ; 163,100 ; 
166,255. He next computed the same three distances 
upon a supposition that tlie orbit was a circle, and 
foimd them to be 148,539 ; 163,883 ; 166,605 ; the 
errors, therefore, of a circular hypothesis, were 
789, 783, 350. But he had too good an opinion of 
Tycho's obseri-ations, (upon which he founded all 
these calculations), to suppose, that the differences 
arose from their inaccuracies ; and as the distance 
between the aphelion and perihelion was too great 
according to the hypothesis in question, he conceived 
that the orbit must be an oval. And, as of all ovals 
the ellipse is the most simple, he naturally made trial 
of this figure, placing the sun in one of its foci ; and 
upon making the requisite calculation, he found the 
agreement complete. He did the same for other 
points of the orbit, and still found the same accurate 
agreement ; and hence he pronounced the orbit of 
Mars to be an ellipse, and that the sun occupied one 
of its foci. Having established this important point 
for the orbit of Mars, he conjectured the same to have 
place in the other planets ; and upon trial he found 
his conjecture fiilly verified : and, hence, he concluded, 
that the six primary planets revolve about the sun in 
elliptic orbits, that body occupying one of the foci. 

Having thus discovered the relative mean distances 
of the planets from the smi, and knowing their periodic 
times, he next endeavoured to find, whefher there were 
any relations between them ; and having naturally a 
strong turn for numerical analogies, he began by com- 
paring the powers of those quantities with each other ; 
and even in the first instance (March 8th, 1616,) he 
assmned the correct law j viz. that the squares of the 
times of revolution are proportional to the cubes of the 
mean distances; but, in consequence of some error in 
his calculation, his comparison did not appear to be 
complete. Nor did he discover it till the folio-wing 
May. He then found his first conjecture to be cor- 
rect, and thus established this celebrated law, which 
Newton afterwards demonstrated to be the necessary 
consequence of a body revolving in an orbit about a 
central attracting point coinciding with one of its foci. 
Prin. Phil. lib. i. sec. ii. pr. 15. 

Kepler also discovered from observation, that the 
velocities of the planets, when in their apsides, are in- 
versely as their distances from the sun ; whence it 
followed, that they described at these points equal 
areas in equal times ; and although he could not 
prove the same for every point of their orbits, he had 
still no doubt that it was so. He therefore applied this 
principle to determine the equation of the orbit ; and 
finding that his calculations agreed with observation, 
he concluded that it was true in general; " that the 
planets describe about the sun equal areas in equal 



Kepler's 
first laiv. 



Kepler's 
second law, 



Kepler's 
third law 



times." This discovery was perhaps the foundation of History. 
the Principia, probably suggesting to Newton the ^— "V"'*** 
idea, that all the planets of our system were governed 
by one general law ! and that the sun was the general 
focus of action ; a proposition which he afterwards 
succeeded in demonstrating, and thus foimded the 
basis of physical astronomy. 

Kepler also speaks of gravity as a power which is 
m^itual between all bodies ; and tells us that the earth 
and moon would move towards each other, and meet 
at a point so much nearer the earth than the moon, 
as the former is greater than the latter, if these motions 
did not prevent it. And he farther adds, that the 
tides rise from the gravity of the waters towards the 
moon. 

The beginning of the 17th century was distinguished Invention 
by two of the naost important events for astronomy of the tele- 
that we have yet recorded ; viz. the invention of the ^"^op^- 
telescope and logarithms ; by means of the one, we 
are enabled to penetrate into the remotest parts of 
space, and to bring under our immediate view pheno- 
mena, which the most sanguine minds could never, if 
they had suspected their existence, have hoped to 
bring within the limits of human observation : by 
means of the other, all the laborious calculations of 
former astronomers were reduced to mere operations 
in addition and subtraction ; and what was before the 
labour of a month, became, as it were, the amuse- 
ment of an hour. With two such powerful auxiliaries, 
the progress of astronomy could not but be extremely 
rapid ; but still the extent to which it has been since 
carried, must certainly far have exceeded what the 
boldest of the astronomers and philosophers of that 
day could have dared to hope for. It never could 
have been contemplated that this science, apparently 
so far beyond the reach of all human power, would 
become the most perfect of all the physical sciences ; 
that every disturbing force, and every celestial pheno- 
menon of our system, should be submitted, with the 
greatest precision, to one general simple principle, at 
that time whoUy unknown ; and that an analysis would 
be discovered, to enable us to investigate and com- 
pute the motion of bodies of immense magnitudes, 
and at almost immeasurable distances, with greater 
accuracy than we can calculate the motion of a pro- 
jectile from a piece of ordnance. Yet such is actually 
the case. We know, to a greater nicety, the moment 
when a planet will arrive at a certain point in the 
heavens, than we can tell the time that a cannon ball 
will employ in passing from the gun to the extremity 
of its destined range, the moment of explosion being 
given. 

As far as we have hitherto traced the progress of Origin of 
astronomy, all our knowledge has been supposed to pl'ysical 
consist in observations on the motions of the heavenly nomy-. 
bodies ; and every species of computation relating to 
it, rested on no other foundation. We are now arrived 
nearly at that period, when our illustrious Newton, 
by his discovery of the law of universal gravitation, 
added ah entire new branch to this important science, 
commonly denominated physical astronomy. From 
this time a greater range was given to celestial re- 
searches ; our knowledge was not confined to the mere 
observation of phenomena, and the return of certain 
bodies to certain parts of space : the causes of these 
phenomena, and of these motions, were now to be 



ASTRONOMY. 



497 



Astronomy, 



Discoveries 
depending 
upon the 
telescope. 



Galileo dis- 
covers the 
satellites of 
Jupiter. 
A.D. 1610. 



investigated, and the amount of them computed from 
the pure principles of celestial mechanics. Every 
minute inequality was henceforward to be traced to 
the same source — tlie action of gravitation : Avhile, 
on the other hand, every minute variation indicated 
by this theory, ought to be observable in the heavens. 
And nothing, perhaps, is better calculated to demon- 
strate the generality of this law, and the beauty and 
profundity of the modern analysis, than the fact, that 
certain small inequalities were indicated by the theory, 
before the accuracy of instruments, and tlie delicacy 
of observation, were sufficiently attained to render 
them appreciable ; but the existence of which, the 
present high state of practical mechanics, and a corre- 
sponding improvement in optics, have confirmed in 
the most satisfactory manner. We shall, therefore, 
now divide the remaining part of this historical 
sketch under two distinct heads ; viz. pi-actical and 
physical astronomy ; and slightly glance at the succes- 
sive steps that have been made in each ; but a simple 
indication of them is all that can be expected, and 
indeed it is all that is requisite, since we must neces- 
sarily meet the same subjects again in the course of 
the following treatise ; where we shall enter upon 
them as much at length, as is consistent with the 
limits allotted to this department of our work. 

Our business here, is neither to give the history of 
the invention of the telescope nor of logarithms ; the 
former has already been treated of in our treatise of 
optics, and the other will be found in its appropriate 
place in this work. We have seen in the article above 
referred to, that the telescope is perhaps an earlier 
invention than it is commonly supposed to be ; and 
that Harriot, in a very early part of the 17th century, 
viz. between the years 1610 and 1613, had actually 
observed the spots on the sun's disc with telescopes 
of various magnifying powers ; a fact, which has been 
but lately ascertained by Baron Zach, of Saxe Gotha, 
who, in a visit to this country, had access to certain 
MSS. of this English author, in the possession of the 
Earl of Egremont, a descendant of the Earl of Nor- 
thumberland, who was Harriot's patron. This, after 
Galileo's, is one of the earliest well attested facts of 
the application of this instrument to astronomical 
purposes. 

Galileo, as we have seen in our history of optics, 
was informed of the accidental discovery of Jansen's 
children, in the year 1609 j and on the Sth of January, 
1610, he perceived, by directing his new instrument 
to the heavens, three small stars near the planet 
Jupiter ; two on the one side, and the third on the 
opposite side ; which he took at first for fixed bodies. 
But having continued to observe them on the next 
and the following nights, he found that they changed 
their places and positions ; and that they performed 
their revolutions about that planet, and were, in fact, 
satellites to it, as the moon is to the earth ; and some 
days after he discovered a fourth. These four satel- 
lites he named, in honour of the house of Medici, the 
Medicean stars ; but the appellation was soon lost in 
the more general and appropriate name of Jupiter's 
satellites. This discovery was published in the month 
of March following, in a writing, entitled Nuncius 
Sydereits ,- he undertook even to investigate the theory 
of their motion ; and, in the year 1613, to predict 
their configurations for two consecutive months. 



Directing his telescope to Saturn, a new surprize. History, 
and new pleasure presented itself. After a few im- V.— -^.^^ 
perfect observations on this planet, he was led to Irregula- 
believe that Saturn was not a simple globe like the '''*y '" *® 
other bodies of our system, but was compounded of g ™ 
three stars touching each other, immovable with 
regard to themselves, and so disposed, that the largest 
occupied the centre, with a smaller one on each side 
of it 5 but it was not long before he discovered this 
idea to be erroneous, so far at least as regarded their 
immobility, or invariable appearance : he found that 
the figure was changeable, but his telescope had not 
sufficient power for him fully to unravel the mystery j 
he found that Saturn appeared irregularly formed, and 
supposed the extreme parts, of what was afterwards 
found to be a ring encompassing the body of the 
planet, were attached to it, forming ansce, or handles ; 
and it was some years after, that Huygens discovered 
the actual conformation of this beautiful telescopic 
object. Galileo also first observed the phases of pjiases of 
Venus, predicted by Copernicus ; as he did also the Venus, and 
spots on the sun's disc, unless indeed our countryman spots on 
Harriot had the advantage of him, in point of time, in ^^^ s"°- 
this observation. There are others v/ho contest with 
Galileo for the honour of the important discovery of 
Jupiter's satellites, as Simon Marius, of Brandebourg, 
who asserts, that he observed them in 1609 ; but the 
truth of this seems to rest on no better foundation 
than the mere declaration of the author, in his 
Nuncius Jovialls, anno 1609, detectus, &c. published in 
1614. The spots on the sun were also observed by other 
Fabricius and Scheiner ; and it is perhaps doubtful by claims for 
whom they were first seen. "The telescope soon these dis- 
became well known in all parts of Europe ; the sun coveries. 
was an object which would naturally claim the regard 
of astronomers, and it is not unlikely these spots 
might be observed by many at nearly the same time. 

The system of Copernicus, even before these dis- Qguigg ^g. 
coveries, had made considerable progress ; and what fends the 
had now occurred, had rendered the truth of it still Copernican 
more certain. Galileo, therefore, in 1615, had the system, 
courage openly to support it ; but it caused him a 
reprimand from the Hobj Inquisition ; he was impri- 
soned, but afterwards liberated upon certain conditions 
of silence. Twenty years afterwards, greater advances 
being made in the progress of this science, he again 
A'entured to assert his opinion, but still with the same 
effect : he convinced all unprejudiced people ; but the 
holy fathers were not in this class, and he was once 
more obliged to abjure upon his knees his heretical 
doctrine. Such are the fruits of ignorance blended 
with bigotry and superstition. 

We shall deviate a little in the order of time, in jiuyo-ens 
order to bring together those discoveries which have discovers 
added to the number of the bodies of the solar system. Saturn's 
Huygens, therefore, according to this arrangement, is ^^ satel- 
the first to claim our attention. This eminent philo- ' ®" ifjoj- 
sopher, having in 1635 constructed for his own use 
two excellent telescopes, the one of twelve, and the 
other of twenty-four feet, discovered a satellite ^o 
Saturn, which is now the sixth in the order of dis- 
tances, and determined the dimensions of its orbit, 
the duration of its revolution, &c. with an astonishing 
degree of exactness ; but falling into a metaphysical 
error, concerning the number of the bodies of our 
system, he sought to find no more, considering that 



498 



A S T R O N O MY. 



Herscliel 
discovers 
the Georgi- 
um Sidus. 



Astronomy, this one was all that was wanting to render the whole 
^— V— ^ planetary scheme complete. He was drawn, however. 
Discovers to a minute examination of Saturn itself, and was the 
Saturn's fj^.gj. ^^ announce the actual conformation of it. He 
""=■ stated, that this planet was encircled by a flat broad 

circular ring, detached from it on all sides, but which, 
according to the position under which it was observed 
from the earth, would assume the several appearances 
of a circle, an ellipse, and a right line ; he never, how- 
ever, observed it under its latter form. He discovered 
that the diameter of the exterior edge of the ring, was 
to the diameter of the planet as 9 to 4 j and that its 
breadth was equal to the space contained between the 
globe and its interior circumference ; results which, 
with some slight modificationSj have been confirmed 
by more modern observations. 
Cassini dis- Four other satellites to this planet were discovered 
covers four by Dominique Cassini : which, in the order of dis- 
Ht'es' ^'''^^" tances, are now the 3d, 4th, 5th, and 7th ; the 5th 
A D^'l6S4 ^"'^ ^^^ "^ 1671, and the 4th and 5th in 1684 ; two 
Herschel Others have since been added by Sir W. Herschel in 
two others. 1789 ; making in all seven attendant luminaries to this 
remote and otherwise solitary planet. 

Eight years prior to the above discovery, viz. in 
1781, Sir W. Herschel had observed a small star, which 
after a little attention, he found changed its place ; 
having well ascertained this fact, he communicated a 
knowledge of the circumstance to M. Laxel, a cele- 
brated astronomer of the academy of St. Petersburgh, 
who was then in London ; the same information was 
also transmitted to other eminent astronomers, who 
observed it with great care, and soon afterwards it was 
announced as a new planet, the most remote in our 
system, circulating about the sun at the astonishing 
distance of nearly eighteen hundred million miles, and 
performing its orbicular revolution in about 80 of our 
years. This new planet was first named by foreign 
astronomers after its observer, the Herschel; but 
Herschel himself, in imitation of Galileo, dedi- 
cated it to his late Majesty, under the name of the 
Georgium Sidus ; both these appellations are, however, 
now nearly become extinct, that of Uranus being 
almost universally adopted. The same indefatigable 
observer has since discovered six satellites to this 
planet, which revolve about him under very peculiar 
circumstances ; but the particulars must be reserved 
for the proper place in the subsequent treatise. 

In order to complete this part of our historical 
sketch, we must now pass to the beginning of the 19th 
century ; the first day of which is remarkable for the 
discovery of another new planet, between the orbits of 
newplaneVs. Mars and Jupiter ; this we owe to the observation of 
Ceres, by Piazzi. This planet has received the name of Ceres. 
Piazzi. Another new planet was ■discovered by Dr. Olbers, on 
the 2Sth of March, in the same year, 180J, which is 
called Pallas ,■ its distance and periodic revolution 
being nearly the same as that of the former. A third, 
having likewise nearly the same mean distance, was dis- 
covered by M. Harding, at Lilienthal, near Bremen, 
September the 4th, 1804 ; and a fourth by Dr. Olbers, 
on the 19th of March, 1807, being the second we 
owe to this indefatigable observer. Of these two, the 
former has been named Juno, and the latter Vesta. 

For the elements, and other particulars respecting 
these new planets, we must refer the reader to the 
respective articles in the following treatise. 



Discovers 
six of its 
satellites. 



Four other 



Pallas, by 
Olbers. 



Jano, by 
Harding. 

Vesta, by 
Olbers. 



Uniting together these several discoveries, it will History, 
appear, that in less than two centuries, there have ^— «v^— ' 
been added to the known bodies of our system, no 
less than five planets, and seventeen satellites, about 
three times as many as were known at the time of the 
promulgation of our present system by its venerable 
author Copernicus. 

In the paragraphs immediately preceding, we have 
in some degree disregarded the order of time, for th« 
purpose of bringing under one point of view those 
discoveries whicli have increased the number of the 
bodies in the solar system ; we must now, therefore, 
retrace our steps, in order to glance at some other 
facts connected with the history of this science ; but 
the bare enumeration of them is all that our limits 
will allow us to attempt. 

In 1603, Bayer formed a catalogue of the stars, f^l^Xe IT 
which he published under the title of Uranometria, the°stars° 
a highly important and useful work. ^.d. 1603. 

Nov. 7, 1G31, Gassendi observed the passage of 
Mercury over the solar disc, agreeably to the predic- Mwra*"^ 
tion of Kepler ; and published his account of it in ^ j, 2.632 
1632, in a work entitled Mercurius in Sole visus, &c. 

1638. The transit of Venus was observed over the Transit of 
sun by Horrox, a young English astronomer^, Avhich Venus, 
is described in his Venus in Sole visus, &c. a.d. 1638, 

These are the two first observations of this kind 
that had ever been made, and much importance was 
in consequence attached to them, although their great 
utility in establishing certain astronomical data was 
not then foreseen. 

In 1638, the sciences had to deplore the loss of Hevelius 
Hevelius, a celebrated astronomer and senator of'^'^'^- 
Dantzic, to whose indefatigable labours we owe many •^•°' lo38, 
valuable observations ; but our limits will not permit 
of our entering into particulars. 

We pass now to that period when the Royal Society Royal So- 
of London, and the Academy of Sciences at Paris, were "^'^'y ^"'^ 
first instituted,and the observatories of Paris and Green- o/scienc s 
wich were erected. The advantage of these institutions 
to the science of astronomy, is unbounded ; instruments 
of the best kind that could be obtained, were immedi- Royal Ob- 
ately constructed : the members of the two academies servatories 
communicated with each other j various experiments °^ London 
were proposed and executed ; and an impulse was ^^^ P^^' 
thus given to science in general, and to astronomy in 
particular, which it would have been in vain to have 
expected from individual perseverance and talent., 
however conspicuous. 

The charter of the Royal Society was granted by 
Charles II. in 1660 ; that of the Academy of Sciences 
by Louis XIV. in 1666. In 1667, the observatory of 
Paris was erected ; and the first stone of the observa- 
tory of Greenwich, was laid by Flamstead (who was 
appointed astronomer royal) on tlie 10th of August, Enrfish as- 
J 675, at the recommendation of Sir Jonas Moore, to tronomers 
whose influence Ave are indebted even for the institu- royal, 
tion itself. Flamstead continued to fill this situation 
in a manner equally honourable to himself and his 
country, for 43 years ; he was succeeded by Dr. Hal- 
ley, who continued in it for 23 years ; Dr. Bradley 
followed Dr. Halley, and held the office for twenty 
years : Mr. Bliss only remained two years, and was 
followed by Dr. Maskelyne, who died in 1811, after 
holding it for 46 years. 

Never has any appointment been more honourably 



ASTRONOMY. 



499 



1 



Astronomy 



Dr. Halley, 



Predicts tlie 
return of a 
comet. 



Roemer. 
A.D. 1667 



Determines 
the velocity 
of light. 



Aberration 
of the fised 
stars. 



. filled than that of the astronomer royal of England. 
' Of the names which we have above enumerated, four 
of them will be handed down to the latest posterity ; 
but we shall only have occasion to refer to Halley and 
Bradley, because we can only nolice the more promi- 
nent features of the history of this science ; and the 
observations and results of the first and last of those 
great men, although of infinite advantage to the at- 
tainment of accurate knowledge, and would therefore 
form an important part in a complete history of 
astronomy, are still not of that striking nature to 
claim more than a general notice in this place. 

Dr. Halley, who was equally celebrated as an an- 
nalyst, a geometer, and astronomer, very early dis- 
tinguished himself by a geometrical method of deter- 
mining the apsides, the eccentricities and dimensions 
of the principal planetary orbits ; he afterwards un- 
dertook a voyage to the island of St. Helena, for the 
purpose of forming a catalogue of the stars in the 
southern hemisphere ; he projected the method which 
was afterwards put in practice for observing the tran- 
sit of Venus in 1761 and 1769, for determining the 
parallax of the sun j and predicted the return of a 
comet in 1759, fixing the period of its revolution at 
75 years ; this comet, which is the only one whose 
orbit is known, and which is expected to reappear in 
1834, bears his name, as an honourable testimony of 
the truth of his prediction, and the profundity of his 
knowledge. Many other valuable works of this 
author we must necessarily pass over. 

In 1667, a highly important discovery was made by 
Roemer, a Danish mathematician, at that time resident 
at Paris. He had long been engaged in making very 
accurate observations on the motion and eclipses of 
Jupiter's satellites ; in the course of which he noticed 
that, at certain times, these bodies emerged from the 
shadow of the planet some minutes later, and at 
others, as much before the time given by the most 
accurate tables. By comparing these variations 
with each other, it appeared, that the satellite emer- 
ged too late from the shadow, when the distance be- 
tween the earth and Jupiter was the greatest, and too 
soon when that distance was the least ; whence, after 
some conjecture, he hit upon the happy idea, that as 
the apparent emersion happened too late or too soon, 
according as the planet was more remote or nearer to 
us, it must proceed from the time that light employed 
in passing over the difference in the two distances ; in 
fact, that the propagation of light is not instantaneous j 
but that it requires a certain time to pass from one 
point to another ; and submitting his ideas to calcu- 
lation, it appeared, that a luminous ray employs about 
eleven minutes in describing a distance equal to that 
of the earth from the sun. This bold idea he commu- 
nicated to the Academy of Sciences on the 16th of 
November, 1667 : it has since been confirmed with 
some modification, reducing the time to 74- minuteS;, 
and has immortalized the name of Roemer. 

Although the system of Copernicus had now gained 
a complete ascendancy, yet many persons were in- 
clined to imagine, that if it were true, some parallax 
ought to be observed in the fixed stars : that these 
bodies should be at such an immense distance, that a 
base of nearly two hundred millions of miles, the diame- 
ter of the earth's orbit, should not sensibly alter their 
positions, waSj it must be allowed, a doctrine suffi- 



cient to startle those who could not expand their History, 
minds to a contemplation of the infinitude of celestial ^— ^^^-/' 
space ; and, accordingly, various observations were 
made with a view of ascertaining whether or not such 
a parallax had place ; and instruments had now arrived 
at that degree of perfection, that it was thought by 
many eminent astronomers such an effect ought to be 
rendered appreciable. 

The minuteness and accuracy of these observations, 
did, indeed, show a small change in the relative posi- 
tion of some stars, but it was, generally speaking, 
directly contrary to that which ought to result from a 
parallax. This motion the cause of which was im- 
known, was denominated aberration ; and it was this 
which Dr. Bradley undertook to examine, and endea- ^'^- Bradley 
voured to reduce to a general law. In the prosecution cau^e'°f *^t° 
of this design, he found that certain stars appeared to ^ ^ i73«' 
have, in the course of a year, a sort of vibration, in ' " 
longitude, without changing their latitude ; some 
varied only in latitude, while others, and that the 
greater number, appeared to describe in the heavens, 
in the course of the year, a small ellipse, more or 
less elongated. This period of a year to which these 
variations answered, although so different from each 
other, was a certain indication that they were con- 
nected v/ith the annual motion of the earth in its 
orbit about the sun ; and after a time, he fortunately 
perceived the cause of all the irregularities he had 
observed. He attributed the apparent aberration of 
the fixed stai-s to the combined motion of the earth, 
and that with which light is propagated. 

Roemer had shown that the velocity of light is 
about 10,000 times greater than that of the earth in 
its orbit , therefore, a ray of light issuing from a star, 
will not carry the impression of this star to the eye, 
till after the earth has sensibly changed its place ; and 
consequently, when the eye receives the impression, 
it ought necessarily to refer the object to a different 
point in the heavens to that in which it is actually 
placed, or to that in which it would appear, if the 
earth were at rest. This explanation satisfied every 
doubt on the subject, and amounted to nearly a ma- 
thematical demonstration of the truth of the Coperni- 
can system. 

We owe to this celebrated astronomer, another dis- Nutation of 
covery no less important than the above, viz, the the earth's 
nutation of the earth's axis. The celestial mechanics ^^'^• 
of our illustrious Newton had sho\vn, that the unequal 
attractions of the sun and moon on the different parts 
of the terrestrial spheroid, ought to produce a varia- 
tion in the position of its axis as referred to the plane 
of the ecliptic. Bradley undertook to examine the 
effect of this motion by means of a long series of deli- 
cate observations, made in those positions of the sun 
and moon most proper to render them manifest. The 
result of his researches were, — 1. That the axis of 
the earth has a conical motion, by which its extremi- 
ties describe about the pole of the ecliptic, and con- 
trary to the order of the signs, an entire circle in 
25,900 years, or an arc of about 50'^ annually. This 
explains the cause of the precession of the equinoxes. 
2dly, That this axis has, with reference to the plane 
of the ecliptic, a libration, by which it inclines about 
18'^ in the course of one revolution of the nodes, and is 
also made contrary to the order of the signs ; after 
which it returns to its first position^ inclines again. 



500 



ASTRONOMY. 



Astronomy, and so on, in each successive period of nineteen years. 
'^-•-V"— ^ Such are the discoveries which render the name of 
Bradley immortal in the history of this science. We 
are also highly indebted to him for numerous other 
important results, to Avhich we shall have occasion to 
refer in the course of the following treatise. 

There still remains one department of practical 
astronomy, which requires to be briefly noticed in 
this sketch, viz. the measurement of the terrestrial 
circumference ; which is important, because the ter- 
restrial radius, in all our actual determination, is the 
only unit of measure to which we can have recourse, 
in order to reduce the ?;everal distances of the heavenly 
bodies to known measures : but as this is also an impor- 
tant datum in the physical branch of astronomy, we 
shall defer the consideration of those measurements, till 
we have to consider it under the latter point of view. 
Progress of We have seen in our account of Kepler, that he 
physical had formed some general ideas of the nature of uni- 
astronomy. versal gravity ; but it was too vague to become the 
Dr. Hook's foundation of any mechanical principle. Dr. Hook, 
ideas of an English philosopher of a most extraordinary genius, 
gravitation, had made a much nearer approximation to a develop- 
A,D. 1668. ment of this great law of the universe. In one of his 
communications to the Royal Society, May 3d, 1668, 
he expressed himself as follows : — " I will explain a 
a system of the world very different from any yet 
received. It is founded on the three following posi- 
tions : 

" 1. That all the heavenly bodies have not only a 
gravitation of their parts to their own proper centres, 
but that they also mutually attract each other within 
their spheres of action. 

" 2. That all bodies having a simple motion will 
continue to move in a straight line, unless continually 
deflected from it by some extraneous force, causing 
them to describe a circle, an ellipse, or some other 
curve. 

"3. That this extraction is so much the greater as 
the bodies are nearer. As to the proportion in which 
those forces diminish by an increase of distance, I own 
I have not yet discovered it, although I have made 
some experiments to this purpose. I leave this to 
others who have time and knowledge sufficient for the 
task." 

This is a very precise enunciation of a proper phi- 
losophical theory. The phenomenon of the change 
of motion, is considered as the ii:!ark and measure 
of a change of force, and his audience is referred to 
experience for the nature of this force : he having 
before exhibited to the society a very neat experi- 
ment, contrived to shew the nature of it. A ball, 
suspended by a long thread from the ceiling, was 
made to swing round another ball, laid on a table 
' immediately below the point of suspension. When 
the impulse given to the pendulum was nicely adjusted 
to its deviation from the perpendicular, it described a 
perfect circle round the ball on the table ; but when 
the impulse was very great, or very small, it described 
an ellipse, having the other ball in its centre. 

Hook shewed that this was the operation of a 
deflecting force proportioned to the distance from the 
other ball ; and he added, that although this illustrated 
the planetary motions in some degree, yet it was not 
suitable to their case ; for the planets describe ellipses, 
having the sun, not in their centre, but in their focus. 



Therefore, they are not retained by a force proportional History, 
to the distance from the sun. V-.-.^-^^/ 

The exalted genius of Newton can suffer no diminu- 
tion by the enumeration of the above opinions ; for 
though the idea of such a principle as gravitation was 
not suggested first by Newton, yet so very obscure were 
the notions of even the most enlightened philosophers 
on this subject, that it had never been successfully 
applied to the explanation of a single astronomical 
phenomenon. 

The important discovery of the law of universal Newton's 
gravitation is so intimately connected with the history discoveries, 
of philoso{)hical science, that every circumstance re- ■*-°' 1666. 
lating to it has been reconled with the greatest care. 
Dr. Pemberton relates, that Newton, in the year 1666, 
having retired from Cambridge to the country on 
account of the plague, was led to meditate on the 
probable cause of the planetary motions, and upon the 
nature of that central force which retained them in 
their orbits ; when it occurred to him, that the same 
force, or some modification of the same force, which 
caused a heavy body with us to descend to the earth, 
might likewise retain the moon in her orbit, by causing 
a constant deflection from her rectilinear path. But 
before this could be submitted to the test of computa- 
tion, it was necessary that some hypothesis should be 
formed relative to the modification of its action with 
respect to distance ; and probably, that which has 
actually place, namely, that it is reciprocally as the 
square of the distance, almost immediately suggested 
itself to his mind, as being observed in all kinds of 
emanations with which we are acquainted. 

When Newton first attempted to verify this con- 
jecture, the requisite data with regard to the distance 
of the moon in terrestrial radii, and the measure of the 
radius itself were but imperfectly known ; the result 
therefore which he obtained, though nearly, did not 
accurately agree with observed phenomena ; and he in 
consequence abandoned his theory as untenable : a 
remarkable instance of the cool and dispassionate 
frame of mind which this great philosopher observed, 
even at the moment when he flattered himself with the 
idea of having discovered one of the most important 
secrets of nature. 

Sometime afterwards, however, he was induced to 
renew his calculations ; as, in the interval, more 
correct data had been obtained by the measurement of 
Picard, in France. This attempt succeeded ; and he 
is stated to have been extremely agitated towards the 
conclusion of his calculation. Whether this were the 
case or not we cannot attempt to settle : at all events, 
a moment of greater interest will never be recorded in 
the annals of science. 

Let us briefly illustrate the nature of the calcula- Principles 
tion to which we have referred. Our author having °f calcula- 
established as a datum, that the distance of the moon '°°" 
from the earth, was about 60 semi -diameters of the 
latter, that is, 60 times as far from the earth's centre 
as a heavy body placed at its surface ; and assuming 
the power of gravity to decrease inversely as the square 
of the distance, it would follow, that at the moon, this 
force would only be one 3600th part of what it is at 
the surface of the earth ; and, consequently, the space 
passed over by a body at this distance, when submitted 
to the terrestrial gravitation, would be only a c'oa of 
that which is actually described here ; or since the 



ASTRONOMY. 



501 



Huygens's 

central 

forces. 



Law of the 

planetary 

motions. 



. spaces are as the squares of the times, and the force 

' inversely as the square of the distance ; the moou 

ought to fall towards the earth through the same 

space in a minute, as a heavy body here describes in a 

second, viz. about 16tV feet. 

Hence it follows, supposing the moon to be retained 
in her orbit by this force, that her deflection from the 
tangent to her orbit at any point, ought to be 160S3 
feet in one minute, or '■#^'^^ in one second. Now the 
distance of the moon from the earth in semi-diameters 
being known, and the radius of the earth itself being 
supposed determined by actual measurement of ter- 
restrial arcs, as also the exact time of one lunar 
revolution, it would be very easy to find the circum- 
ference of the lunar orbit, and the measure of the arc 
which the moon describes in one second, whence again 
the versed sine of that arc, or the difference between 
the secant and radius, which is nearly the same thing, 
may also readily be obtained in feet ; and this, as 
above observed, ought to be St-t"- This measure 
Newton verified by his calculation, and thus esta- 
blished this most important law with regard to the 
earth and moon, which was afterwards readily extended 
to the whole planetary system. 

Several years before this discovery of Newton's, 
Huygens had given in thirteen propositions the pro- 
perties of centrifugal and centripetal forces in a circle ; 
but he did not think of applying his theory to the 
motion of the earth on its axis, and to the moon about 
the earth ; had he done this, it is highly probable he 
would have arrived at the same conclusion as Newton ; 
this grand step in his process was, however, wanting, 
and the entire honour of the discoA'ery justly devolved 
upon our illustrious countryman. 

In order to extend the same principles to the other 
planetary motions, Newton was led to consider, that 
when two bodies act on each other by attraction, the 
action is reciprocal ; moreover, that the attraction of 
each body is equal to the sum of the attraction of all 
its parts, and therefore proportional to the mass ; con- 
sequently, some other data were requisite for demon- 
strating that the whole system was regulated by this 
one general principle ; — the motion of the moon 
appertaining only to the earth, while the earth and all 
the other planets revolved about the sun. 

Newton demonstrated, generally, that if a body 
projected into space be continually turned from its 
direction, by any force which urges it towards a fixed 
centre, and which causes it to describe a curve, the 
areas of the sectors comprised between the arc of the 
curve and the right lines joining the body and fixed 
centre, are proportional to the times of description, 
and vice versa, if the areas are proportional to the 
times the revolving body is necessarily urged towards 
a fixed centre. Now the primary planets observe this 
law in revolving about the sun ; therefore regarding 
this body as fixed, it follows, that each planet is con- 
tinually attracted towards the sun as a centre. But 
from this condition alone he wotild have been able to 
determine nothing respecting the nature of this force. 
Kepler, however, furnished the law necessary for this 
determination ; for if to the condition of equal areas 
being described in equal times, we add the other con- 
dition, that the orbit is an ellipse, then it will 
follow, as demonstrated by Newton, that the force 
must vary reciprocally as the square of the distance. 



Still, however, this only proved that the law obtained Historv. 
for each planet individually in different parts of its 's,*— .^^-i.^ 
orbit, and it still remained to be shown that the same 
had place for every planet in the system ; viz. that 
each was attracted by a force which was reciprocally 
as the square of its respective distance. Here again 
another datum of Kepler's was of the highest import- 
ance ; he had shown that the squares of the periodic 
times were as the cubes of the distances ; and this 
was sufficient for demonstrating the universality of the 
law in question j namely, that every material particle 
in nature attracts with a force proportional to its mass, 
and reciprocally as the square of its distance from the 
body on which it acts. It is this law which regulates 
all the planetary motions, and to which we must have 
recourse for explaining any irregidarities observable 
in them. 

Our planetary world is compounded of different Masses of 
systems : thus the sun and the primary planets may certain pla- 
be considered as one system, the earth and moon as '^^.'^ deter- 
another, Jupiter and his satellites as a third, and so on ; ™'"^ * 
and it will be necessary to distinguish between these, 
when we are comparing the motions of bodies in one 
of those systems with those in another ; the mass of 
the central body being a necessary datum in deter- 
mining the actual motion of the circulating body ; 
and conversely, the motion of two or more revolving 
bodies being known, the masses of the attracting 
bodies may be determined. It was thus Newton 
found, that, denoting the mass of the sun by unity, 
that of Jupiter would be expressed by the fraction 
-nh-Ty Saturn by -Wr-r, and the earth by -rynhs^- 

We cannot follow Newton through the numerous 
inferences, calculations, and deductions, which re- 
sulted from this universal law 5 it will be sufficient to 
observe, that it accounted for the flux and reflux of 
the tides, the nutation of the earth's axis, the preces- 
sion of the equinoxes, the spheroidal figure of the 
earth, and various irregular motions in the planetary 
system ; but some of these have been illustrated and 
submitted to calculations within the last few years, 
in a manner more exact and conclusive tlian in the 
time of our author. Analysis has taken a much 
greater range, and every advance that it has made, 
has furnished some further confirmation of the truth 
and generality of the great law of universal gravitation. 

If there were but two bodies in our system, as, for Difficulty of 
example, — the sun and earth ; or but three, — the sun, tlie general 
earth, and moon, the determination of their actual problem, 
and disturbing forces on each other would be compa- 
ratively a problem of easy solution ; but when we 
consider the influence of several bodies, whose posi- 
tion with respect to each other is perpetually chang- 
ing, and then endeavour to estimate tlieir effects on 
any one in particular, we shall find the question 
involved in the greatest perplexity, and apparently far 
beyond the reach of human intellect to comprehend ; 
yet such has been the progress of analysis within the 
last half century in the hands of D'Alembert, Euler, 
Lagrange, La Place, and some others, that not a 
single phenomenon now remains, nor the smallest 
irregularity in the motions of the principal bodies of 
our system, that is not accounted for ; its amount 
computed, and its origin traced to that law which it is 
the glory of Newton to have first discovered. 

As these subjects must necessarily come before us 
3 T 



■H 



I 



502 



ASTRONOMY. 



Different 
measures 



Figure of 
tlie eartli. 



Astronomy, in our treatise on physical astronomy, we sliall not 
V— — ^^— —^ detain the reader with the nature of the particular 
solutions and investigations of the autliors above 
alluded to ; but shall pass on to the only remaining 
topic — tlie figure and magnitude of the earth. 
Magnitude We liave seen that this problem had been attempted 
and figure by Eratostlienes, and again by the Arabian mathemati- 
oftheeartL, cian Almamon, but we know very little of their deter- 
minations ; we may however easily imagine, knowing 
how great the difficulty of the operation is, even Avith 
the most perfect instruments, that their approximations 
must necessarily have been very reniote from the 
truth ; and probably the early attempt's of tliis kind 
in Europe vi^ere not attended with much better success. 
We shall briefly notice tliose which seem to be of 
the greatest importance. 

In 1525, M. Fernelius measured a degree of the 
meridian northward from Paris, which he made 
687634 English miles. Snellius, professor of mathe- 
matics at Leyden, and our countryman, Norwood, 
measured each of them a meridional degree ; the 
former in Holland in 1620, and the latter in England 
between London and York, in 1635. Snellius' mea- 
sure, when reduced to English miles, is 6691 ; and 
tliat of Norwood 69545 miles. In 1644, Riccioli also 
undertook a similar task, and performed it according 
to three different measures, between mount Parderno 
and the tower of Modena in Italy, and obtained a 
mean lengtli of 75'066 English miles to a degree. 

These results differed too much from each other to 
inspire the least confidence in any of them, and conse- 
quently nothing could thence be deduced respecting tlie 
figure of the earth ; nor was this indeed, at that time, 
suspected to be any other than a perfect sphere, abstract- 
ing from the irregularities on its surface. But after the 
construction of the telescope had received consider- 
able improvement, and when observations had been 
reduced to greater nicet)^ it was found that the planet 
Jupiter was considerably flattened at his poles ; and 
the pendulum experiment of Richer, 1671, had shown 
tliat there was a difference in the action of gravity at 
the equator and in the latitude of Paris ; and these two 
circumstances probably first suggested to Huygens 
that the earth was not spherical ; and its rotatory 
motion about its axis naturally led him to conclude 
that it was flattened at its poles ; from the combination 
of its centrifugal force with that of gravity, he calcu- 
Determined lated that its polar axes were to its equatorial diameter 
as 578 to 579. But as he regarded all the power of 
terrestrial attraction to be collected in the centre of 
the earth only, his solution was obviously defective ; 
and Newton soon after undertook the same determi- 
nation, on more correct principles, by supposing every 
particle in the whole mass to have a reciprocal attrac- 
tion towards all the others ; from which he found 
the figure to be an ellipsoid, having its polar and 
equatorial diameters to each other at 229 to 230. 
Determined In this state the question remained for many years, 
by practical till M. Picard undertook the measurement of a degree 
measure- ^^ France, in 1669, which was afterwards revised by 
Cassini in 1718 ; the result of which tended to show, 
that the earth was not an oblate but a prolate sphe- 
roid. Picard obtained for the length of a degree 
68'945 English miles, and Cassini 69'119,- whereas 
the latter, being the most southern, ought to have 
been the shortest. A circumstance so unexpected as 



by Newton 
and Huy 

gens. 



this, naturally produced a great curiosity, and a con- History. 
siderable degree of inquiry and controversy between "s-.->y— i^ 
the astronomers and mathematicians of that period ; 
and the French government, at the recommendation 
of the Academy of Sciences, in 1735, sent out two 
companies of mathematicians to determine the point 
in question, by measuring two degrees, one at the 
equator, and the other in as high a northern latitude 
as possible. Accordingly, MM. Godin, Bouguer, and 
Condamine, from France, with Dons Juan and UUoa, 
from Spain, proceeded to Peru ; while Maupertuis, 
Clairaut, Camus, La Monnier, &c. accompanied by 
Celsus, a Swedish astronomer, proceeded to Lapland, 

After experiencing many unforeseen difficulties and 
delays, both parties accomplished the object of their 
missions, and returned to France ; those from Lap- 
land in 17373 and the other division in 1744. The 
former made the length of their degree, the middle 
point of which was in latitude 66° 20^, equal to 69-403 
English miles ; while at the equator the length, as 
determined by the other party, was found to be 68-724 
English miles, taking the mean of three different 
results, deduced from the same operation. In the 
interval betvi^een the outfitting of the above expedi- 
tions, and the publication of their results, the degrees 
of Picard and Cassini were examined, recomputed, 
and found now to be, the first, whose middle point 
was in latitude 49° 22', 69' 121 English miles, and 
other 69092 miles, its middle point being 45°, 

The results therefore of all these measures confirmed Oblate fi- 
the earth to be an oblate spheroid ; but as they were gure esta- 
compared together in pairs, they gave very different tilished. 
degrees of ellipticity ; nor has all the accuracy that 
has since been introduced into these operations been 
sufficient to establish this point. Colonel Mudge in 
England, has measured an arc extending from the sou- 
thernmost point in the kingdom to the northernmost 
of the Shetland islands ; and Messrs. Delambre, Ellipticity 
Mechain, Biot, Arago, &c. have carried another still uncer- 
from Dunkirk to Fomentara, one of the Balearic isles, tain, 
It is perhaps never to be expected that greater 
accuracy can be introduced into any operations, nor to 
see greater talents employed in conducting them, 
than in the cases to which we have last referred ; and. 
yet these tvm measures, compared with each other, in 
different portions, give very different ellipticities ; 
different parts of the same arcs give very discordant re- 
sults J even some of those of the English survey, are 
such as to lead again to the idea of the prolate figure 
of the earth. What are we then to conclude from the 
whole of these deductions, but that the irregularities of 
local attraction, or some other causes which we can- 
not discover, produce a certain influence or disturbing 
power, which renders useless the comparisons of small 
arcs, and that those results only can be depended ion 
that are drawn from measurements that extend tl ^^h 
several degrees of latitude. Adopting this prini,iple, 
we may state, that the mean length of a degree in the 
latitude 45° is 68769 English miles, and that the 
ellipticity of the earth is between ^-^ and ■^+^. 

One other point still requires to be alluded to before 
we conclude our history. It was observed by Bou- 
guer, in his operations in Peru, that the high moun- 
tains in some parts of that country, very sensibly 
disturbed the verticality of his plumb-line ; that is, 
the lateral attraction drcAv the line out of its per- 



Medlum re- 
sults. 



ASTRONOMY. 



503 



Astronomy, pendicular direction, a certain quantity which he 
\,»->^^-i^ determined. This suggested to the Royal Society 
the idea of employing this deflection, in order to as- 
Density of certain the actual density of the earth as compared 
the earth. -^Hh water, or any other known substance. In order 
to this, it was necessary to select some isolated moun- 
tain, whose density and magnitude might be ascer- 
tained ; when by observing how much a pendulum or 
plumb-line was deflected on opposite sides of it, at 
given distances, the proportional forces between the 
earth and mountain would become known, and hence 
from the established laws of attractions, the relative 
masses of the two bodies would be determined, and 
hence tlie density of the earth, its magnitude being 
supposed already ascertained. 

The mountain selected for this purpose was Sche- 
hallian, in Scotland, and Dr. Maskelyne, in 1742, was 
requested to direct the operations. The mean height 
of Schehallian above the surrounding valley is about 
2000 feet, and its direction is nearly east and west. 
Two stations were chosen for observation, one on the 
north, and the other on the south side of the moun- 
tain. Every circumstance that could contribute to 
the accuracy of the experiment, was attended to with 
particular care ; and from the observations on ten 
stars near the zenith, Dr. Maskelyne found the appa- 
rent diiference of the latitudes of the stations to be 54' 
6" : and from a measurement by triangles from the 
two bases, on different sides, he found the actual dif- 
ference of their parallels to be 4364 feet, which, in the 
latitude of Schehallian, 56^ 40^, answers to an arc of 
the meridian of 43', which is less, by 11' 6", than that 
found by the sector. Tliese data being submitted to the 
calculation indicated above, a task which was performed 
by Dr. Hutton, it ajipeared thatthedensity of the whole 
mass of the earth as compared with water, was nearly 
in the ratio of 44- to 1. Phil. Trans, vol. 65, and vol. 68 ; 
but from more accurate observations on the geology 
of this mountain by Playfair, it appears that there was, 
in the first instance, some error in assuming its den- 
sity ; and the corresponding reduction being made in 
Dr. Hutton's determination, gives the density of the 
earth 495, that of water being 1 ; which more nearly 
agrees with the determination of Mr. Cavendish, who 
on other principles, which are explained m the Phil. 
Trans, for 1798, makes it 5-48.* 

We have now ^iven, it is presumed, a sketch of all 
the more prominent points connected with the history 
of astronomy ; much highly important matter is, we 
are aware, also either wholly passed over, or very 
slightly alluded to ; but to have noticed all the cir- 
cmnstances worthy of record would have carried us 
far beyond our proposed limits ; moreover, many of 
the minutiae we shall have occasion to refer to in our 
ilh ration of the various topics in the following 
tr« e ; where we shall also take the opportunity of 
inti-oducing the titles of some of the more important 
and useful works on this subject, and to which we 
would refer our readers for the attainment of a perfect 
knowledge of the ancient and present state of astro- 
nomical science. 

* In the last volume of the Phil. Trans. Dr. Hutton has given a 
paper on this suhject, pointing out certain eiTors of calculation in 
Mr. Cavendish's Memoir ; and which, when corrected, make the 
result more approximative to the last determination of this vener- 
able mathematician. 



Plane Astronomy. Plane 

Astronomy. 
§ II. Introduction. — Containing a popular view andillus- '^ _.- __' 
tration of the most remarkable phenomena of the hea- 
vens, 

1. General remarks. 

] . Astronomy differs very essentially from all other introduc- 
mathematical sciences, with regard to the connection tion. 
of its propositions, and the force of its demonstrations. 
In geoiTietry, for example, after the requisite defini- 
tions have been laid down, and certain axioms and 
postulates granted, the reader finds no farther claims 
made upon him for the admission of this or that hypo- 
thesis ; he judges for himself at every step ; and 
every step furnishes him with some new" truth, as cer- 
tain and incontestable as his own existence. So also, 
in theoretical mechanics : our investigations, if they 
do not always preserve the same concatenation, 
as in geometry, furnish an equal conviction to the 
mind of the reader, because he is never required to 
give his assent to a proposition, till the means are 
prepared to rest its demonstration upon something 
previously established. 

In astronomy, on the contrary, a student is called 
upon for the admission of an hypothesis v/hich is con- 
trary to the evidence of his senses. While he and 
every thing about him are in a state of apparent 
permanent rest, he must admit that they are moving 
with an inconceiviible velocity ; and on the other 
hand, that those bodies, which, judging from his senses 
only, he supposes to be in rapid motion, are actually 
at rest ; moreover, he must wait till the whole chain 
of reasoning is established before he will be able to 
judge, and to be convinced of the truth of the hypo- 
thesis which he has previously admitted. He Avill 
then at least feel this conviction, viz. if the law of 
gravitation, and the constitution of the solar system 
were such as he has assumed, that every phenomenon, 
the most important as well as the most minute, would 
happen exactly in the same manner as they actually 
do ; and hence, he will be able to judge of the high 
degree of probability, that the supposition he has 
made is strictly and positively correct. 

To mention a few of the most prominent facts, we pa^tg g^ 
may observe, that the law of gravitation, and the hy- Which the 
pot'hesis of the earth's rotation on its axis, render it truth of the 
highly probable, that the terrestrial globe is not a modern as- 
perfect sphere, but an oblate spheroid ; and the va- /g^^J 
rious geodetic operations that have been carried on in 
diff"erent countries, leave no longer any doubt that 
such is its actual figure. Again, the same hypotheses 
indicate, that the intensity of gravity ought to be 
different in different latitudes ; not merely in conse- 
quence of the figure of the earth, but on account of 
the difference in the centrifugal force in different 
latitudes ; and therefore, that the seconds pendulum 
ought to be longer at or near the poles, than at the 
equator ; and that such is truly the case, has been 
demonstrated by various experimeats. The aberra- 
tion of the stars, the nutation of the earth's axis ; the 
precession of the equinoxes : phenomena, whose exist- 
ence have been ascertained by observation, are inex- 
plicable upon any other supposition ; and to this we 
may add, that of all the minute inequalities which the 
accuracy of modern instruments, and a corresponding 
3t2 



504 



ASTRONOMY. 



Astronomy, delicacy of observation have rendered appreciable in 
\,„„~y.,^^ the motion of the planetary bodies, there is not one 
of them but what is immediately shown to be the ne- 
cessary consequence of the law of uniA'ersal gravitation, 
and the assumed constitution of the solar systein. 

These facts, and many others which we might have 
advanced, if they do not amount to actual demonstra- 
tion, necessarily involve in them such a high degree 
of probability as falls very little short of it ; leaving 
on the mind a conviction little inferior to that which 
we derive from absolute certainty. 

This conviction, liowever, as we have before ob- 
served, cannot be felt till the entire chain of reasoning 
has been established ; till this is effected, some doubt 
may be allowed to remain on the mind of the student ; 
he will, it is true, as he advances, find greater and 
more substantial reasons for admitting the truth of 
his hypothesis, but he will not feel complete satisfac- 
tion till he is able to compare and weigh the whole. 
Sketch of 2. In the following sketch, therefore, which we have 
tUearrange- given of the constitution of the solar system, we do 
ment of the not require the implicit assent of the reader ; we 
several sub- ^jgl^ j^jj^ only to consider wliat we have stated, as 
^ ■ the enunciation of a proposition, or of a chain of 

propositions, of which we shall endeavour, step by 
step, to demonstrate the truth ; nor shall we attempt, 
in the first instance, to give the particulars with the 
utmost nicety ; because this is unnecessary, where 
we wish simply to indicate a general view of the 
planetary motions ; but in the subsequent part of our 
treatise, we shall exhibit only the most modern and 
authentic results. We shall enter upon our subject, 
on the supposition that our reader is wholly unac- 
quainted with even the first principles of the science, 
and therefore that he requires an explanation of every 
phenomenon. This explanation we propose to render 
in the first instance merely popular, viz. without at- 
tempting any but the most simple computations ; for 
example, we shall first illustrate the most remarkable 
celestial phenomena, the changes of season, the alter- 
nation of night and day, the phases of the moon and 
planets, the general principles of eclipses, &c. &c. 
Having thus indicated to the student, the first prin- 
ciples of the science, and given him a concise view of 
what we propose to establish ; we shall then describe 
to him the circles of the sphere, the construction of 
some of the most indispensable astronomical instru- 
ments, introduce him to the observatory, and point 
out to him the nature of the observations that are 
necessary as the groundwork of his computations. 
These observations, however, will stand in need of 
certain corrections, the cause and quantity of which 
he must therefore be next instructed in j after which, 
he will find no difficulty in following us through the 
remaining part of this division of our subject. 

Having said thus much with reference to the plan 
we propose to follow in this treatise, we shall begin 
by exhibiting a brief description of the stars, and of 
the constellations into which they have been divided. 

2. Of t]te fixed stars. 

Of the fixed 3. It is impossible to conceive a more magnificent 

Btars. spectacle, nor one more worthy of the contemplation 

of an intelligent being, than that which is presented 

to our view by the starry firmament in an unclouded 

sky; a few hours after the setting of the sun. We 



then observe innumerable brilliant points spread in Plane 
every direction over the azure canopy of the heavens ; Astronomyi 
various in magnitude and lustre ; differently disposed ^•— v"-— ^ 
with regard to each other, and arranged in groups 
to which the imagination will readily attribute nume- 
rous ideal forms and characters. 

If this scene be attentively observed for some suc- 
cessive nights, it will be perceived that the greater 
number of those bodies preserve constantly the same 
relative position with regard to each other ; to these 
therefore has been given the name of Jixed stars. 
Others of them are perpetually changing their places, 
varying in their lustre, and apparently traversing dif- 
ferent circles of the celestial space ; these are, there- 
fore denominated, wandering stars or planets ; while a 
third class, much more rare in their appearance, and 
totally distinct from aU others in their figure and . 
motion, are sometimes observed, surrounded by a 
faint sphere of light, and followed by a like luminous 
train, which at times extend over a considerable arc 
of the celestial vault. This sphere of light, from its 
supposed resemblance to hair, has given to these 
celestial visitants the name of comets. These three 
classes of bodies will form the subject of distinct 
chapters in the course of this treatise ; at present our 
business is to take a popular view of the fixed stars, 
in order to illustrate the important uses to which they 
are applied, both in practical and physical astronomy. 

4. One of the first objects of a student in this science Divisionsof 
should be to make himself acquainted with the names the stars in- 
and situations of the most conspicuous stars and con- ^° . constel- 
stellations ; the latter being a term used to denote ^^^^°^^- 
those groups of stars which are supposed to have 

some resemblance in their form to the animal or other 
objects, whose names they bear. The division of the 
stars into constellations is of very remote antiquity ; 
and though it may be useless, and sometimes even 
inconvenient, for the ptn-pose of minute observation ; 
yet for a general recollection of the great features of 
the heavens, these arbitrary names and associations 
cannot but greatly assist the memory. It is also 
usual to describe particular stars by their situation 
with respect to the imaginary figure, to which they 
belong, as Spica Virginis, Cor Hydrce, &c. or more 
commonly at present, by the letters of the Greek 
alphabet, which were first applied by Bayer in 1603, 
and in addition to these by the Roman letters, and by 
the numbers of particular catalogues. 

5. The stars are again divided into different classes or Apparent 
magnitudes, according to the degrees of their apparent magnitudes;, 
brightness. The largest or most vivid of which, are 

said to be of the first magnitude ; the next in order of 
brightness of the second, and so on to the sixth, which 
latter class includes all those that are barely percep- 
tible to the naked eye ; all of a smaller kind, are 
generally called telescopic stars, being invisible without 
the assistance of the telescope. 

In order to become familiar with the names and Method of 
positions of the principal stars and constellations, the acquiring a 
student must place himself in an open situation, where ^"rt^'^f^ 
he can observe the whole of the celestial hemisphere ; 
he will then perceive, after an attentive observation of 
their motion, that certain of the stars exposed to his 
view, will, after attaining their greatest altitude, de- 
cline and sink below the horizon ; others will attain 
to ttie meridian, descend again, but will not sink 



ASTRONOMY. 



505 



represent- 
ing the 
stars. 



Astronomy, below the horizon ; and by directing his view with 
^-*~V"'™^ attention towards that part of the heavens Avhere this 
occurs, he will perceive some few stars, and one in 
particular, which have no perceptible motion : this 
latter is called the pole star, because it is about an 
axis passing A^ery near to this, that the apparent 
motion of the heavens takes place. The place of this 
star referred to the horizon is called the north, the 
opposite point the south, that to the right hand the 
east, and to the left the west. 
Different 6. There are two principal modes of representing 

methods of the stars ; the one by delineating them on a globe, 
where each star occupies the spot in which it would 
appear to an eye placed in the centre of the globe, 
and Avhere the situations are reversed when we look 
down upon them ; the other mode is by a chart, 
where the stars are generally so arranged as to repre- 
sent them in positions similar to their natural ones, 
or as they would appear on the internal concave sur- 
face of the globe. 

In acquiring a knowledge of the particular stars, it 
will be most convenient to begin with such as never 
set in our climates ; after which, we may readily refer 
the situations of others to their position Avith respect 
to these. 

7. The Great Bear is the most conspicuous of the 
constellations, which never set in our latitude ; it 
consists of seven principal stars, placed like the 
four wheels of a v/aggon, and its three horses, 
except that the horses are fixed to one of the wheels. 
Their con- The hind wheels are called the pointers, because they 
nectioas, direct us to the pole stai, in the extremity of the 
tail of the Little Bear ; and further on to the con- 
stellation Cassiopeia, vifhich is situated in the milky 
way (See Plate I. Astronomy,) which consists of 
several stars nearly in the form of the letter W ; or 
we may easily imagine them to represent a chair; 
whence these few in particular form what is more 
commonly called Cassiopeia's Chair. 

The two northernmost wheels of the Great Bear, 
or Wain, point at the bright star Capella, in 
Auriga. Descending along the milky way from 
Cassiopeia, if we go towards Capella, we come to 
Algenib, in Perseus, and a little further from the 
pole Algol, or Medusa's Head ; but if we take the 
opposite direction, we arrive at Cygnus, the Swan, 
and beyond it, a little out of the milky way, is the 
bright star Lyra. The Dragon consists of a chain 
of stars, partly surrounding the Little Bear; and 
between Cassiopeia and the Swan, is the constellation 
Cepheus. 

Near Algenib, and pointing directly towards it, are 
two stars of Andromeda, and a third is a little beyond 
them, A line drawn through the Great Bear and 
Capella, passes to the Pleiades, and then turning at a 



Different 
constella- 
tions. 



&c, 



right angle towards the milky way, reaches Aldeba- Plane 
ran, or the bull's eye, and the shoulder of Orion, who -^^stronomy. 
is known by his belt, consisting of three stars placed """V""^ 
in the middle of a quadrangle. Aldebaran, the Plei- 
ades, and Algol, make the upper end, Menkar, or the 
whale's jaw, with Aries, the lower point of a W. In 
Aries we observe two principal stars, one of them 
with a smaller attendant. 

A line from the pole, midway between the Great 
Bear and Capella, passes to Gemini, the twins, and to 
Procyon ; and then in order to reach Sirius, it must 
bend across the milky way. Algol and the Twins 
point at Regulus, the lion's heart, which is situated at 
one end of an arch, with Denabola at the other end. 

The pole star, and the middle horse of the wain, 
direct us to Spica Virginis, considerably distant : the 
pole and the first horse, nearly to Arcturus in the 
waggoner, or Bootes. ISIuch further southward, and 
towards the milky way, is Antares in tlie Scorpion ; 
forming, with Arcturus and Spica, a triangle, within 
which are the two stars of Libra. The northern 
crown is nearly in a line between Lyra and Arcturus ; 
and the heads of Hercules and Serpentarius are be- 
tween Lj'ra and Scorpio. In the milky way, below 
the part nearest to Lyra, and on a line drawn from 
Arcturus, through the head of Hercules, is Aquila, 
making, with Lyra and Cygnus, a conspicuous tri- 
angle. The last of the three principal stars in Andro- 
meda, make, with three of Pegasus, a square, of which 
one of the sides points to Fomalhaut, situated at a 
considerable distance in the southern fish, and in the 
vicinity of the whale, which has been already mention-: 
ed. By means of these supposititious lines, all the prin- 
cipal stars that are ever visible in our climates may be 
easily recognised. Of those which never rise above 
the horizon, there are several of the first magnitude ; 
Canopus in the ship Argo, and Achernar in the river 
Eridanus, are the most brilliant of them ; the feet of 
the Centaur, and the Crosier are the next ; and, 
according to Humboldt's observations, some others 
perhaps may require to be admitted into the same 
class. See Plate 11. 

The constellations to which we have above referred, 
are divided into three principal classes ; those on the 
northern side of the equator are called northern con- 
stellations, and those on the opposite, southern con- 
stellations ; while those wliich are situated in that 
part of the concave hemisphere where the principal 
planets and other bodies of our system are observed 
to move, forming a zone, which crosses the equator 
in two points, are called zodiacal constellations. The 
names of these, Avith the number of stars belong- 
ing to each, in four of the principal catalogues ; the 
names of the principal stars ; and the characters of 
the zodiacal constellations, are as follow : — 



506 



A S T R O N O M Y. 



Table of the Constellations, 
Zodiacal. 



Names and Characters of the Constellations. 


Number of Stars in 


different Catalogues. 


Principal Stars. 






Ptolemy. 


Tycho. 


Hevelius. 


Flamstead. 




Mag. 




r the Ram 


18 


21 


27 


66 








Q the Bull 


44 


43 


51 


141 




1 
1—2 


Gemini 


n the Twins 


25 


25 


38 


85 


Castor and Pollux 


Cancer 

Leo 


S the Crab . ... 


13 


15 


29 


S3 






^ the Lion, with Coma 




Berenices 


35 


30 


49 


95 


Regulus 


1 


Virgo 


tij^ the Virgin 


32 


33 


50 


110 


Spica Virginis . . 


1 


Libra 


£h the Scales 


17 


10 


20 


51 


Zubenich Meli . . 


2 


Scorpio 


. i7|^ the Scorpion 


24 


10 


20 


44 


Aatares 


1 


Sagittarius . 


f the Archer 


31 


14 


22 


69 






Capricornus. 
Aquarius . . . 


Vf the Goat 


2S 


28 


29 


51 






-: the Water Bearer . , 


45 


41 


47 


108 


Scheat 


3 


Pisces 


J< the Fishes 


38 


36 


39 


113 







Northern Constellations. 



Names of the Constellations. 



Ursa ]Minor, the Little Bear 

Ursa Major, the Great Bear 

Perseus 

Auriga, the Waggoner 

Bootes 

Draco, the Dragon 

Cepheus 

" Canes Venatici, viz. Asterion et Chara 
the Greyliounds 

* Cor Caroli 

Triangulum, the Triangle 

* Triangulum Minus 

* Musca 

* Lynx 

* Leo Minor, the Little Lion 

* Coma Berenices, Berenice's liair .... 

* Camelopardalus 

* Mons Menelaus 

Corona Borealis, the Northern Crown. . 
Serpens, the Serpent , . . 

* Scutum Sobieski, Sobieski's Shield . . 
Hercules, cum Ramo et Cerbero 

Hercules, since called Engonasia 

Serpentarius, sive Ophiuchus 

* Taurus Poniatowski 

Lyra, tlie Harp 

*Valpeculus et Anser, the Fox and Goose 

Sagitta, the Arrow 

Aquila, the Eagle, with Antinous. . . . 

Delphinus, the Dolphin 

Cygnus, the Swan 

Cassiopeia, the Lady in her Chair .... 
Equulus, the Horse's Head 

* Lacerta, the Lizard 

Pegasus, the Flying Horse 

Andromeda 



Number of Stars in different Catalogues. 



Ptolemy. 
8 
35 
29 
14 
23 
31 
13 



Tycho. 

7 
29 
29 

9 
18 
32 

4 



12—3 

10 

18 

26 

4 



Herelius. 
12 
73 
46 
40 
52 
40 
51 

23 



Flamstead 
24 
87 
59 
66 
54 
80 
35 

25 

3 
16 
10 

6 
44 
53 
43 
58 
11 
21 
64 

8 

113 

74 
7 
22 
37 
18 
71 
18 
81 
55 
10 
16 
89 
66 



Principal Stars. 



Pole-star . 
Dubhe . . . 
Algenib . 
Capella. . . 
A returns . 
Rastaber . 
Alderamin 



Ras Algiatha 
Ras Alhagus 



ega 



Altair 

Deneb Adige 



.ALarkab 
Almaac 



Mag. 



Those constellations distineTiished * are new constellations. 



ASTRONOMY. 

Southei'n Constellations. 



5o; 



Names of the Constellations. 



*PhcEnbc 

* Officina Sculptoria , 

Eridanus 

* Hydrus, the Water Snake 

Cetus^ the Whale 

* Fornax Chemica 

* Horologium 

* Reticulus Rhomboidalis 

* XiphiaSj Dorado, the Sword Fish: . , , 

* Celapraxitellis 

Lepus, the Hare 

* Columba Noachi, Noah's Dove .... 

Orion 

Argo Navisj the Ship , 

Canis Major, the Great Dog 

* Equuleus Pictorius 

* Monoceros, the Unicorn 

Canis INIinor, the Little Dog 

* Chamaeleon ^ . . , , 

* Pyxis Nantica 

* Piscis Volans, the Flying Fish ...... 

Hydra 

* Sextans 

* Robur Carolinum, the Royal Oak. . . , 

* Machina Pneumatica 

Crater, the Cup 

Corvus, the Crow 

* Crosiers, et Cruzero 

Apis Musca, the Bee or Fly 

*Apus, or Avis Indica, the Bird of Paradise 

Circinus, the Compass 

Centaurus, the CentaTir . . . , 

Lupus, the Wolf . . t 

' Quadra Euclidis ; . . . . 

Triangulum Australe^ the Southern 

Triangle 

Ara, the Altar . . . 

Telescopium 

Corona Australis, the Southern Crown 

Pavo, the Peacock 

Indus, the Indian 

Microscopium 

Octans Hadleianus 

* Grus, the Crane 

Toucan, the American Goose 

Piscis Australis, the Southern Fish . . . 



Number of Stars in different Catalogues. 



Ptolemy. 
34 



27 



Tyehc 

10 
21 



10 



Flamstead. 
13 
12 
84 
10 
97 
14 
12 
10 

7 
16 
19 
10 
78 
61 
31 

8 
31 
14 
10 

4 

8 
60 
41 
12 

3 
31 

9 

6 

4 
11 

4 
35 
24 
12 

5 

9 

9 
12 
14 
12 
10 
43 
14 

9 
24 



Principal Stars. 



Achernar 
Menkar , 



Betelgense 
Canopus . . 

Sirius . . . . 
Procyon , . 
Cor HydrjB 

Alkes .... 



Fomalhaut 



Mag, 
1 



Total Number of Constellations. 



Zodiacal 12 

Northern 34 

Southern 45 

91 



Number of Stars in each Magnitude, British Catalogue. 



1st Mag. 
5 
6 
9 

20 



Mag. 
16 
24 
36 

76 



3d Mag, 



223 



4th Mag. 
120 
200 
190 

510 



5th Mag. 
183 
291 

221 

695 



6th Mag. 
646 
635 
323 

1604 



Plane 
Astronomy. 



1014 
1251 
863 



i 



508 



ASTRONOMY. 



Astronomy. 8. It appears from the preceding summary of the stars 
*^— <— y— «-^ in the British catalogue, that the number of them in 
Number of the entire celestial sphere, including all those of the 
toXnakcd ^^^^^ magnitude, does not much exceed 3000 ; and it 
eye.^"^ ^ ^^ generally stated, that not more than 1000 are ever 
visible at one time to the naked eye : but when a 
telescope is employed, their number appears to in- 
crease without any other limit than that of the per- 
fection of the instrument. SirW. Herschel has observed 
Milky way. in the milky way above 10,000 stars in the space of 
one square degree. This luminous track 

" Which ni2:htly, as a circling zone, thou seest 
Powder'd with stars," 

encompasses the heavens, and forms nearly a great 
circle of the celestial sphere. It traverses the con- 
stellations Cassiopeia, Perseus, Auriga, Orion, Ge- 
mini, Canis Major, and the Ship, where it appears 
most brilliant ; it then passes through the feet of the 
Centaur, the Cross, the southern Triangle, and returns 
towards the north by the Altar, the tail of the Scor- 
pion, and the arc of Sagittarius, where it divides into 
two branches, passing through Aquila, Sagitta, the 
Swan, Serpentarius, the head of Cepheus, and returns 
to Cassiopeia. The ancients had many singular ideas 
respecting the cause of this phenomenon, but modern 
astronomers have long attributed it to an immense 
assemblage of stars too feeble to make distinct impres- 
sions ; and Herschel has shown, by the observation 
above referred to, that these conjectures were well 
founded. 

Besides the milky way, there are numerous other 
parts of the heavens, which exhibit an appearance of 
Nebulae. very nearly the same kind, which are called Nebulce; 
the most considerable of which is that midway between 
the two stars in the blade of Orion's sword. This 
was first observed by Huygens ; it contains only seven 
stars ; the other part appearing like a luminous spot 
upon a dark ground, or like a bright opening into 
regions beyond. 
Proper mo- 9. We have hitherto spoken of the fixed stars, as 
tion of preserving actually the same relative situations with 
some stars, j-gg^rd to each other ; this, however, is not strictly 
true. The delicacy of modern observations has shown 
that some of these bodies have a progressive motion : 
Arcturus, for example, has a proper motion, amount- 
ing to about two seconds annually ; and Dr. Maskelyne 
found, that out of 36 stars, of which he ascertained 
the places with great accuracy, 35 of them had a pro- 
gressive motion. 

Mr. Michell and Sir W. Herschel have conjectured 
that some of the stars revolve round others which are 
apparently situated near them ; and perhaps even all 
the stars may in reality change their places more or 
less, although their relative situations, and the direc- 
tion of their paths may render their motions imper- 
ceptible. 
Variable That some of the stars have a periodical change of 

stars. brightness has been well ascertained from repeated 

observations ; and different hypotheses have been 
advanced to account for these singular phenomena. 
New stars have also appeared at certain times, re- 
mained stationary like the others, and have afterwards 
disappeared. Such a temporary star was observed by 
Hipparchus ; and it was this circumstance which 
suggested to him the idea of forming a catalogue of 



them, and of delineating their situations. A nevv Plane 
star was also discovered in Cassiopeia in 1572, which Astronomy. 
was so bright as to be seen in the day-time, but it ^"-""W^^^ 
gradually disappeared in 16 months. Another was 
observed by Kepler in 1604, more brilliant than any 
other star or planet, and changing perpetually into 
all the colours of the rainbow, except when it was 
near the horizon. This star remained visible about 
a year ; and several other cases of the like kind are 
recorded. 

As to the actual magnitude and distance of the Distance 
stars, we may be said to be almost wholly unac- and magni- 
quainted with either ; all that we are able to state ^^^^ "'^' 
with certainty is, that their distance is immense. We ''°°^'*- 
shall show, in a subsequent chapter, that the distance 
of the sun from the earth is nearly 100 million miles j 
and, consequently, the diameter of our orbit is nearly 
200 million miles ; we therefore view the stars, or 
any one of them in particular, from two points at 
different times of the year, which are distant from 
each other 200 million miles, and yet we are not 
able to detect any difference in their apparent places. 
If a change of place, amounting only to one second, 
actually obtained, there is no doubt that it would be 
detected by the accuracy of modern observations ;* 
we know, therefore, that an isosceles triangle having 
the diameter of the earth's orbit for its base, and 
having its vertex in the nearest fixed star, does not 
subtend an angle of one second ; the nearest star 
must therefore be distant from us more than 20 
billions of miles. How much their distance may ex- 
ceed this, it is impossible for us to say; and much, 
less are we able to offer even the most distant con- 
jecture as to their actual mag-nitude ; judging from 
analogy, we can only suppose them to be bodies 
resembling our sun, some of greater, and some of less 
magnitude ; that they shine like the sun by their 
own light, each forming the centre of its particular 
system, dispensing light, heat, and animation to 
thousands of worlds, and to myriads of beings. 
What a wonderful idea do these reflections give us of 
the immensity of the universe, and of the power and 
omniscience of the great Creator and Director of so 
stupendous a machine ! 

3. Of the Solar System. 
10. The system of Copernicus has been already refer- The solar 
red to in our historical chapter. We have seen, that, system, 
according to this astronomer, all the principal planets 
revolve about the sun as a general, but not as a com- 
mon centre ; the several planets being supposed by 
him to describe circular orbits, each however having 
its particular point of circulation. The Copernican 
and the modern system are not therefore the same, 
although these terms are frequently employed synoni- 
mously. We shall here confine our description to the 
modern or true system, without, however, deducing 
any facts in proof of its accuracy : we shall be content 

* It is proper to observe, that since this was written. Dr. 
Brinkley, of Trinity College, Dublin, has been led to think, that 
he has detected a sensible parallax in several stars ; but as Mr. 
Pond, the Astronomer Royal, has not yet been able to verify Dr. 
Brinkley's observations, we do not feel ourselves justified in stating 
the existence of a parallax ; although, from the confidence we 
feel in the talents and accuracy of the observer, we have no doubt 
that his deductions will be hereafter verified by other astronomers. 



ASTRONOMY. 



509 



planets. 



Astronomy, that the reader receives it at present merely as an 
^-•'-V-"-^ hypothesis, or rather as the enunciation of a propo- 
sition ; and that he suspends his decision, till, in the 
course of the following chapters we advance such 
proofs as can leave him no longer in any doubt re- 
specting the constitution of the solar system, nor of 
the mechanical principles on which its motions depend. 
The sun is The sun has probably, as well as every body in the 
the central universe, a progressive motion in space ; but if such 
^"^y- a motion has place, he is accompanied in it with the 

whole system of which he forms the general centre, 
as well as the source of its light, heat, and motion ; 
■we may therefore consider this body at rest, as far as 
regards the relative motion of the other constituents 
of our system. 

The sun, then, according to the modern hypothesis 
occupies a fixed centre, about which the several prin- 
cipal planets revolve, in elliptic orbits, one foci of each 
of which is found in tlie same point, coinciding very 
nearly with the solar centre. Several of these planets 
are again accompanied with attendant luminaries, 
which observe the same laws in their revolutions 
about their primaries, as these primaries do with 
respect to the sun. 
Inclination 1 1 . The orbits of the several planets are not all situated 
of the orbits in the same plane, biit are variously inclined to each 
of the other, and to a fixed plane passing through the sun, 

called the plane of the ecliptic. Even this plane is 
not actually fixed, but is subject to a certain annual 
motion, to which, however, we shall not refer in this 
description. The several planets of our system, Avith 
the exception of the four small ones lately discovered, 
have their inclinations very small ; the particular 
measures of which will be stated belo-.v ; and their 
Motion of motions are all made in one direction, viz. from west 
the planets, to east. Several of these bodies are also known to 
Inclination have a rotatory motion on their respective axes, but 
of their these axes are differently inclined with respect to the 
axes. plane of the ecliptic, each, however, always preserving 

its own direction parallel to itself. This rotatory 
motion is likewise performed from west to east, at 
least in all those bodies in which it has been hitherto 
observed ; but some, either from their immense dis- 
tance, their inconsiderable magnitude, or from their 
proximity to the sr.n, have not yet had their diurnal 
revolution decidedly ascertained. 
Eccentrici- 12. The orbits of the planets we have seen are all 
ties of the • elliptical, but these ellipses have very different degrees 
of eccentricity ; that is, the ratio of the major and 
minor axes vary very considerably in tlie orbits of the 
different planets. The orbits of the satellites have also 
various eccentricities, and are differently inclined to 
the ecliptic, and to each other ; in some of the secon- 
daries this inclination is extremely great, while in all 
the principal bodies of our system it is very inconsi- 
derable. 

These general remarks being premised, we shall 
proceed concisely to describe the particular circum- 
stances attending the motion of each planet, beginning 
with the sun, and proceeding orderly with the other 
bodies, according to their respective distances from 
him. 
Of the sun. 13. The sun, which is known to be 882,270 English 
miles in diameter, performs its diurnal revolution in 
25 days 14h. 8', about an axis, which is inclined 82° 
3(y from the plane of the ecliptic. 

VOL. III. 



orbits. 



14. Mercury is the nearest planet to the sun ; its mean Plane 
distance is about 36 millions English miles ; the time Astronomy. 
of its sideral revolution 87 days 23h. ; its diameter ^— -^v—^ 
3123 miles ; the inclination of its orbit to the eclip- Mercury, 
tic, 7° 0' 9" ; and the ratio of the eccentricity of its 

orbit to that of its semi major axis '2055149. The in- 
clination of its axis is unknown, and the time of its diur- 
nal revolution doubtful ; it has been stated at 24h. 5'. 

15. Venus is the second planet in order from the sun j Venus, 
her mean distance being 68 millions of miles, and the 
time of her sideral revolution 224 days 16 hours. 

The diameter of this planet is 7702 English miles j 
the inclination of its orbit 3° 23' ; and the ratio of its 
eccentricity to the semi major axis of its orbit -0068529. 
Its diurnal revolution is performed in 23h. 21', about 
an axis, which, like that of Mercury, is of unknown 
inclination. 

16. The Earth is the third planet in the system ; its The Earth, 
distance from the sun is 93 million miles, and the 

time of its sideral revolution 365 days 6h. 9' ; which 
must not be confounded with the length of the solar 
year, this being only 365 days 5h. 48' 48" ; the dia- 
meter of this planet is 7916 miles. The orbit of the 
earth being that to which the plane of the other 
planetary orbits are referred, its inclination is nothing ; 
the eccentricity of its orbit is •0168531 ; its diurnal 
revolution is performed in 23h. 56m. 4", (which is 
called a sideral day), about an axis which inclines to 
the ecliptic in an angle of 66° 32' 3", the complement 
of which, viz. 23 27' 57", is the obliquity of the ec- 
liptic as referred to the equator. 

17- The next primary planet in our system is Mars ; its Mars. 
mean distance from tlie sun is 142 millions of miles, 
and its sideral revolution is performed in 686 days 
234-h. ; its diameter is little more than half that of the 
earth, being only 4398 miles. 

Its orbit is inclined to the ecliptic in an angle of 
1°51'3"3 the eccentricity of its orbit is -0931340, 
and its diurnal revolution is performed in 24h. 39m., 
about an axis, which is inclined to the plane of the 
ecliptic at an angle of 59° 41' 49". 

18. The next planets in order from the sun, are the Vesta, 
four new ones ; Ves>ta, Juno, Ceres, Pallas, of which lit- Juno, 
tie is known, except their times of revolution, and the Ceres, 
inclination of their orbits ; and these may even here- ^^' 
after be found to stand in need of some corrections : 
they are at present stated as follows : — 

Vesta 5 mean distance, 225 million miiles ; time of 
sideral revolution, 1335 days 4h.5 inclination of orbit, 
7° 84' ; eccentricity, -0932200. 

Juno ; mean distance, 253 million miles ; period of 
sideral revolution, 1590 days 23h. j inclination of 
orbit, 21° J eccentricity, -254944. 

Ceres ; mean distance, 263 million miles ; period 
of revolution, 1681 days 12h. ; inclination of orbit, 
10° 37' ; eccentricity, -0783486. 

Pallas ; mean distance, 265 million miles ; period 
of revolution, 1681 days 17h. ; inclination of orbit^ 
34° 50' ; eccentricity, -245384. 

The diameters of tliese planets (which must, how- 
ever, be considered as doubtful,) have been given as 
follow : — ^Vesta, 238 miles ; Juno, 1425 miles ; Ceres, 
1024 miles ; and Pallas, 2099 miles. 

1 9 . Jupiter, the largest of all the planets of our system, Jupiter, 
is the next after Pallas ; its mean distance from the 

sun is 485 million miles, and its diameter is 91522 
3v 



510 



ASTRONOMY. 



Ui'anus, c 
Georgium 
SiJus. 



Astronomy, miles, more than ele^'en times that of the eai-th : the 
^i^-^y——^ inclination of his orbit to the ecliptic is 1° 18' 51'', 
and his sideral revolution 4,332 days 14 hours, the 
ratio of its eccentricity to the semi major axis •0481784. 
Tlie diurnal revolution of Jupiter is performed in 9 
hours .55' 49", about an axis which is inclined to the 
ecliptic at an angle of 86° 544-'. 
Saturn. ^0. Saturn is next to Jupiter, as well in magnitude 

as in distance ; the latter being 890 million miles, and 
its diameter 76,068 miles ; his sideral revolution is 
performed in 10,758 days, or about thirty of our years, 
and the eccentricity of his orbit -0561683. The diur- 
nal revolution of Saturn is made in 10 hours 16 19", 
about an axis which is inclined to the ecliptic at an 
angle of 58° 41'. 

21. Last in the solar system is the Georgium Sidus, 
or Uranus ; whose mean distance is more than double 
that of Saturn, being no less than 1800 miUion miles ; 
its diameter is 35,112 miles, and the eccentricity of 
its orbit -0446703. Its sideral revolution is per- 
formed in about eighty of our years : but its diurnal 
revolution, and the inclination of its axis, are not at 
present determined. 

22. We have endeavoured to represent, the planetary 
distances, eccentricities, and proportional magnitude 
in Plate III., with the exception of the sun, which is 
there represented nearly as a point, whereas, in com- 
parison with the magnitude we have given to the 
planets, its diameter ought to have exceeded even 
that of the orbit of Saturn. The several orbits in 
the plate are all represented as if situated in one 
plane ; it is necessary therefore for the reader to bear 
in rnind the measures of the several inclinations above 
indicated. 

23. The following are the characters or symbols em- 
ployed by astronomers for denoting the several 
planets : — 



The Sun 


o 


Ceres 


? 


Mercury 


5 


Pallas 


^ 


Venus 


? 


Jupiter 


% 


The Earth 


© 


Saturn 


^ 


Mars 




Uranus 


¥ 


Vesta 


® 


The Moon 


D 


Juno 


f 







Characters 
of the pla- 
nets. 



24, At present we have spoken only of the prima.ry 

planets, it now remains for us to say a few words with 

reference to the satellites by which some of them are 

attended. 

The moon. The first, and that which in this place claims our 

particular attention, is the moon, which revolves 

about the earth, as the earth itself does about the 

sun. Her mean distance from the terrestrial centre 

is 237,000 miles ; her diameter is 2,160 miles, and 

the eccentricity of her orbit is -0548553. The period 

of her orbicular and diurnal revolutions, are exactly 

alike, being completed in 27 days 7 hours 43' 4"-7. 

The inclination of her orbit is 5° 9', and of her axis 

88° 29' 49". 

Satellites of It is unnecessary in this place to enter into the 

Jupiter, Sa- same minutia; with respect to the other satellites ; it 

turn, &c. ^.-^Yl be sufficient to observe, that Jupiter has four, 

Saturn seven, and Uranus six, as represented in the 

plate above referred to. 

Saturn's Besides the seven satellites which accompany Sa- 

ring. turn in his dreary path, he is also encompassed by a 

double ring, by which he is distinguished from all 



the other planets of our system. This ring, which is Rane 
very thin, not exceeding 4,500 miles, is inclined to Astronomy. 
the plane of the ecliptic at an angle of 31° 19' 12", *^— -^y^^ 
and revolves from west to east in 10 hours 29' 16"-8 ; 
this rotation is performed about an axis perpendicular 
to the plane of the ring, passing through the centre of 
the planet. 

We shall not enter more particularly in this place 
into a description of this singularly beautiful telescopic 
object ; as we shall of course have to treat of it at 
length in a subsequent chapter, in which we shall state 
its several dimensions as determined from the best 
observations ; it will be sufficient here to observe, 
that its outside diameter is 204,883 miles, and its 
inside 146,345, consequently, its mean breadth is 
about 30,000 miles. 

25. We come now to the third class of bodies, which Comets, 
are only visible to us for a short time. The planets per- 
form their revolutions about the sun within the limits 
of our observation, and at distances from him which 
vary comparatively very little in the different parts of 
their orbits ; but those to which we now refer, if 
they all actually revolve about the sun, are, for a 
very considerable time far beyond the known limits 
of the solar system. These are called comets : they 
generally appear attended with a nebulous light, either 
surroimding them as a coma, or stretched out to a 
considerable length as a tail, and sometimes they 
appear to consist of such light only. Their orbits are 
so eccentric that in the remoter parts of them they 
are invisible to us, although at other times they ap- 
proach much nearer to the sun than any of the planets : 
the comet of 1680, for example, when nearest the 
sun, was at the distance of only one sixth of the sun's 
diameter from its surface. Their tails are frequently 
of great extent, appearing as a faint light directed 
tOAvards a point always opposite to the sun. It is 
quite uncertain of what matter they consist, and it is 
difficult to say which of the conjectures concerning 
them is the least improbable. Nearly 500 comets are 
recorded as ha\dng been seen at different times, and 
certain particulars relative to the orbits of about a 
hundred of them, have been accurately ascertained : 
but commonly, we have no opportunity of observing 
a sufiicient portion of the cometary path, to determine 
■with accuracy the entire dimensions of the ellipse or 
other conic section to which the observed part ap- 
pertains ; on which account little can be known of 
the periods and other circumstances of these wan- 
dering bodies. Only one comet has been recognized 
in its return to our system, which is that of 1759. 
Dr. Halley, by comparing together the elements of 
the several comets that had been observed up to his 
time, conjectured tliat those recorded to have appeared 
in 1531, in 1607, and in 1682, were, in fact, one and the 
same comet, and, consequently, that its return might 
be expected about the year 1758 or 1759, and its 
actual appearance in the last of those years, verified 
the conjecture. Another comet, which appeared in 
1770, was suspected to move in an elliptic orbit ; and 
if so, its period ought, by Mr. Lexel's computation 
(which has been since remade by Burckhardt), to be 
about 5 years and 7 months ; it has never, however, 
been since observed ; but this circumstance miist not 
lead us to discredit either the observations made on 
it^ or the calculations founded on them, for it has 



ASTRONOMY. 



511 



Astronomy, been satisfactorily shown, that supposing all the data 
^^^•"s^j.-mJ correct, this comet must have passed so near to Ju- 
piter, that its orbit would be deranged, and the body- 
rendered in future invisible to us. 

We shall not enter further on the subject of comets 
in this place, except to observe, that whether their 
orbits be all ellipses, or some of them parabolas or 
hyperbolas, a very small portion of them fall within 
the limits of our system ; if they are all ellipses, they 
are of very great eccentricity, and are only for a short 
period visible in these regions of celestial space. The 
orbits of two of these bodies are shown in our Plate III. 

4. Phenomena in tlie heavens, due to the motion of the 
earth and planets. 
Diurnal ^*5. We have already in our second section given a 

motion of general view of the celestial sphere, with an enumera- 
the earth, tion of the several constellations ; we propose now 
to illustrate a few particular phenomena, and to de- 
scribe certain circles which astronomers have ima- 
gined for the better comprehension of the celestial 
motions. 

We have seen that a person being situated in an 
open plane, in a star light evening, and watching at- 
tentively the motion of the fixed stars, will perceive 
them rise or emerge above the earth, continue to 
ascend, till they have attained a certain height, and 
then descend and disappear in the opposite side of 
the heavens to that in which they first rose. He will 
perceive, that accordingly as these stars are nearer 
the northern or southern points of the heaven, so they 
will appear visible to him for a greater or less time ; 
and that certain stars very near the north point, never 
either rise or set, but would be always visible were not 
their light rendered imperceptible by the more refulgent 
rays of the sun. 

One of the stars in this quarter of the heavens, to 
which we have already alluded, has scarcely any sen- 
sible motion, but, as far as the naked eye can distin- 
guish, retains constantly the same situation ; this 
is called the pole star, and those to which we have re- 
ferred above, that appear to be constantly circulating 
about it, are, for that reason, called, circumpolar stars. 
Apparent The first impression that this apparent motion of 
motion of the stars would make on the mind of an uninformed 
theheavens. observer would be, that the entire celestial vault was 
uniformly revolving from east to west, about an ima- 
ginary axis, which passes through or near the pole 
star, in a direction perpendicular to the planes of the 
circles described by the several stars which are alter- 
nately observed to rise and set; and consequently, that 
this line produced would again meet the celestial 
sphere in an opposite point, which may thence be de- 
nominated the south pole. This, as we have observed, 
would doubtless be the first impression made on an 
uninformed observer ; but at the same time, if he 
possess the requisite intelligence, it would not be dif- 
ficult to convince him that the very same appearances 
would be produced by supposing the earth to be of a 
globular form, and that it performed a motion of ro- 
tation about an axis corresponding with the supposed 
axis of the heavens, but in an opposite direction, that 
is, from west to east; numerous instances might be 
recalled to his recollection in which he had appeared 
at rest, when he was actually in rapid motion, and 
when objects were apparently seen to move with 



great velocity, although they were in fin absolute state plane 
of rest. This phenomenon must have presented itself Astronomy, 
to every one who has travelled in a close carriage in ^^ — y*— ' 
a narrow road, when at times it is difficult to be per- 
suaded but that the trees, gates, &c. which we pass 
are not moving in an opposite direction to that of the 
vehicle ; and the same appearances are observed still 
more strikingly in the cabin of a ship when sailing 
with a moderate gale near the land. In fact, every 
intelligent observer, whether he admits the actual 
motion of the earth or not, will not for a moment 
deny, that if it had such a motion as we have sup- 
posed, the appearances would be exactly such as he 
observes in the heavens. This then will be one step 
towards his conviction, and various others will after- 
wards suggest themselves to his mind ; which, how- 
ever, we shall not at present insist upon, because from 
what has been stated, it is obvious, that we may at 
any rate be allowed to advance such an hypothesis as 
the diurnal revolution of the earth, without in any re- 
spect changing the appearance of any observed phe- 
nomenon. We shall therefore proceed upon the sup- 
position of the earth being a sphere or a spheroid of 
small ellipticity, and that it performs a motion of rota- 
tion from west to east in about 24 hours ; or rather, 
as we shall see in a subsequent chapter, in 23 hours 
56'4'''l. 

27. By observing attentively the stars which first ap- Apparent 
pear visible in that part of the heavens where the sun motion of 
sets, and continuing to observe them for several sue- the sun. 
cessive nights, we shall soon perceive that those stars 
which in tlie first instance we had observed to set imme- 
diately after the sun, are no longer to be seen, but that 

their places are supplied by certain others, which in 
their turn will also be lost in the solar beams. If 
nov/ we observe the heavens in the morning before 
the rising of the stm, we shall find that those stars 
which in the first instance we had observed to set just 
after the sun, and which in the course of a few nights 
were absorbed by his rays, are now rising before him ; 
the sun therefore has made an apparent motion in the 
heavens contrary to the general motion of the stars, 
that is, from west to east; and by following his pro- 
gress in this manner during the course of a year, we 
shall find that he has described a complete circle of 
the heavens, and now rises and sets with the same 
star as we had observed exactly a year before. This 
circle which the sun thus appears to describe in the 
heavens is called the ecliptic, it is not directly east and 
west, but deviates nearly 24° from these points of the 
heaven, as shown in Plates I. and II., and to his obli- 
quity it is, that we owe the variations in the seasons, 
and various other phenomena, as Ave shall show in a 
future chapter. 

28. This progressive motion of the sun in the hea- rpjjjg ^ 
vens, which is only apparent, is due to the actual rent motion 
proper motion of the earth in its orbit about the sun. of the sun 
For let AB (Plate IV., fig. 1) represent two positions is due to 

...S;f A-Rr oK..nf fhP c„n S Ae proper 



of the earth 



its orbit ABC about the sun S, 



and let T^ 0^ 11, 95, &c. represent the ecliptic or the earth, 
the apparent path of the sun. Then when the earth Fig. 1. 
is at A, a spectator will refer that body to that part 
of the heavens marked r ; but when the earth is 
arrived at B, he will then see it in EI ; and being in 
the mean time insensible of his own motion, the sun 
will appear to him to have described the arc T Jl> 
3 u3 



512 



ASTRONOMY. 



Astronomy, just the same as if it had actually passed over the arc 
V— — y— »»^ SS', and the earth had;, during that time, remained 
quiescent in its first position A. This fact will ex- 
plain why certain remarkable stars and constellations 
are seen in the south in different seasons of the year, 
and at different hours of the night. For the hour 
depends wholly on the sun ; it is noon when the sun 
is south, and midnight when it is north ; the stars 
directly opposed to him will therefore, by the rotation, 
appear in the south about midnight ; and as the sun, 
from one day to another, shifts its place in the hea- 
vens, so, of necessity, will different stars be opposed 
to him, and become south at midnight at different 
seasons of the year. 
Proper 29. Similar phenomena may be observed with regard 

motion of to the planets ; by tracing their motions in the heavens, 
the planets, and comparing them with the stars near to which they 
appear, they will also be seen to ha-se a motion of 
their own, but it will be more irregular than that of 
the sun ; for we shall sometimes observe them mov- 
ing like that body from west to east, then become 
stationary, maintaining the same position for several 
nights ; then moving in a contrary direction, or from 
east to west 5 again become stationary, and again 
assume their direct motion. 

These phenomena, which the ancients spent so much 
labour and ingenuity to account for, by epicycle upon 
epicycle, are perfectly consistent with the system as 
we have described it in our third plate, being due to 
the proper motions of the earth and planets in their 
respective orbits. In order to illustrate this, let 

V v' v" represent the orbit of the planet Venus ; and 
suppose her to be in the point v when the earth is at 
A 5 then it is obvious that a spectator will refer her 
place in the heavens to T, and as her motion is from 

V towards v' , while the earth is moving from A to B, 
her apparent motion will be direct ; or from T to- 
wards : if, on the other hand, Venus had been at 
v" while the earth was at A, as their motions now 
are made in the same way, we may suppose Venus to 
have arrived at v'" , while the earth had passed from 
A to A' 5 and during this time, it is manifest her place 
in the heavens will appear to retrograde, or go back- 
ward, contrary to the order of the signs : in like 
manner it will appear, that for a very short time 
before and after the Earth and Venus attained their 
positions A and v" , their motions would so agree with 
each other, that the planet, during this period, 
would appear stationary. We shall enter more at 
length upon these phenomena in a subsequent chap- 
ter ; we have merely referred to the subject here, to 
show that these appearances are strictly conformable 
with the constitution which we have supposed of the 
solar system. 

Notwithstanding these irregularities in the apparent 
motion of the planets, they each, respectively, are 
observed to describe great circles of the sphere, but 
more or less inclined to the plane of the ecliptic j 
they deviate, however, but little from it ; aU their 
motions, with the exception of the new planets, being 
performed in a zone, whose breadth does not exceed 
16 degrees, and which we have already spoken of 
and described in our first and second plates, under the 
denomination of the zodiac. 

Similar observations show that the moon also 
- describes her particular path amongst the stars j 



but we shall reserve this subject for a subsequent Plane 
chapter. Astronomy. 



5. Of the Seasons. ^ 

30. It will appear sufficiently obvious from what has Of the 
been shown in the preceding sections, that the alter- seasons, 
nations of day and night are attributable generally to 
the rotation of the earth on its axis ; but the differ- 
ence in the length of the days in differeht seasons of 
the year stiU remains to be illustrated. 

We have seen that the two extremities of the ter- Equator 
restrial axis about which the diurnal rotation is per- defined, 
formed, are called its poles, as N S, (fig. 2 and 3) ; Fig- 2, 3. 
and if at a quadrant distance from these we conceive a 
circle QEQ' to be described, dividing the earth into 
two equal hemispheres, that circle is called the equa- 
tor ; the hemisphere towards the north pole N is 
called the northern hemisphere ; and that towards the 
south pole, the southern. Now if the path of the Consc- 
earth in its orbit, or, which is the same, the apparent quenccs 
motion of the sun in the heavens coincided .with the *^j'' ^°'i''^ 
plane of the terrestrial equator, then it is obvious, (ijg Jquator 
that, at all times during this revolution, we should and ecliptic 
have the same equal alternations of day and night, coincided, 
each 12 hours in duration. For example : let NQSQ' 
represent the earth ; NS, its axis ; and QEQ', its equa- 
tor : and let the plane of this circle produced pass 
through the sun S j then it is obvious, that, if we 
suppose the earth to revolve round the sun at the 
extremity of the line SE as a radius ; and that during 
this revolution, it performed uniformly its rotatory 
motion about its axis NS : that line, NS, or the circle 
of which it is the projection, would terminate the 
limits of day and night ; and the rotatory motion 
being uniform, every point of the globe, except the 
two poles, would have an equal succession of light 
and darkness during the entire revolution. We should 
then have no spring, no summer, no winter ; these 
changes so pleasing in themselves, and so necessary 
for the production and re-production of the fruits of 
the earth would be wanting, and nature would thus 
be divested of a great portion of its, charms. 

This, however, is not the case ; we have seen that Conse- 
the sun appears to describe an oblique motion in the quences of 
heavens ; it rises higher in the summer than in the ^^^. °^^\- 
winter, and by thus darting upon us more perpendi- ggjjptjg 
cularly its refulgent beams, produces a greater por- 
tion of heat, and describes a larger circuit in the 
heavens, lengthens out the days, and thus gives time 
for that heat to become more effective. 

The actual motion of the earth is therefore as re- 
presented in (fig. 3,) where we 'still, suppose it to 
describe its annual motion at the extremity of the 
radius S'TE ; but such, notwithstanding, that the axis 
NS preserves its inclination and parallelism, whereby 
it is always directed to the same point in the heavens. 
The axis NS being now inclined to the plane of the 
earth's motion, it is obvious, that, as it revolves on 
its axis, some parts of the earth wiU experience per- 
petual day for a certain portion of the year, while 
other parts will have to contend with an equal du- 
ration of night. In the position of the earth, as shown 
in the figure, the parts about the north pole wiU be 
in continued darkness, and those near the southern 
pole in perpetual light ; while, from the nature of 
the annual motion^ it is clear that it will be exactly 



ASTRONOMY 



513 



Astronomy, 



Illustrated 
by experi- 
ment. 
Fig. 4. 



the reverse when the earth shall have attained the 
, opposite point of its orbit ; the regions of the south 
pole will then be involved in darkness, and those of 
the northern will enjoy their return of light, as will 
appear obvious by supposing the sun to be transferred 
to the other side of the earth, which is exactly equi- 
valent to the change of place in the earth. 

31. Dr. Long, in his astronomy, gives us a pleasing 
illustration of this change of the seasons, with the 
variable lengths of the days and nights, by means of 
the following experiment :-- 

Take about seven feet of a strong Avire, and bend 
it into a circular form, as bed, (fig. 4,) which being 
viewed obliquely, appears elliptical, as in the figure. 
Place a lighted candle on a table, and having fixed 
one end of a thread K to the north pole of a small 
terrestrial globe H, about three inches in diameter ; 
cause another person to hold the wire circle, or fix it 
so that it may be parallel to the table, and as high as 
the flame of the candle I, which should be in or near 
the centre ; then having twisted the thread as towards 
the left hand, it will, by untwisting, turn the globe 
round eastward, or contrary to the way which the 
hands of a watch move ; hang the globe by the thread 
within the circle, nearly contiguous to it ; and, as 
the thread untwists, the globe, which is enlightened 
half round by the candle as the earth is by the sun, 
will turn round its axis, and the different places upon 
it will be carried through the light and dark hemi- 
sphere, and have the appearance of a regular succes- 
sion of days and nights, as our earth has in reality by 
such a motion. As the globe turns, move the hand 
slowly, so as to carry the miniature earth round the 
candle according to the orders of the letters a, b, c, d, 
&c., keeping its centre even with the wire circle, and 
it will be perceived, that the candle, being still per- 
pendicular to the equator, or rather in the plane of the 
equator produced, it will enlighten the globe from 
pole to pole, as we have shown in fig. 2, and that 
during the whole of its orbicular revolution; conse- 
quently every place on the globe goes equally through 
the light and dark, as it turns round by the untwisting 
of the thread. The motion of the globe turning in 
this way represents the earth revolving on its axis ; 
and the motion of the same in the circle of wire, its 
revolution round the sun ; and shows, that if the orbit 
of the earth had no inclination to its equator, all the 
days and nights in every part of the globe would be 
of equal duration throughout the year, as described in 
the first of the preceding figures. 

Now desire the person who holds the wire to incline 
it obliquely, in the position ABCD, raising the side 
ffi just as much as he depresses the side yf , that the 
flame may be still in the plane of the circle ; and 
twisting the thread as before, that the globe may turn 
round its axis the same way as you carry it round the 
candle; that is, from Avest to east. Let the globe 
down into the lowermost part of the circle yf ; and if 
the latter be properly inclined, the candle will shine 
perpendicularly on the globe at a, and the region 
about the north pole will be all in the light, as shown 
in the figure, and will still keep in the light while 
the globe revolves on its axis. 

From the equator to the north polar circle, all the 
places have longer days and shorter nights ; but from 
the equator to the north pole just the reverse takes 



place — the niglits being longer than the days. The piane 
sun does not set to any part of the northern frigid Astronomy, 
zone, as is shown by the candle constantly shining ^^^--y-^ 
upon it while the globe is in this position : and on the 
same principles, it will appear that the southern arctic 
regions are, during this time, involved in constant 
darkness ; the revolution of the globe never bringing 
any part of it within the illuminated hemisphere ; and, 
therefore, if the earth remained constantly in this 
part of its orbit, the sun would never set in the 
northern frigid zone, nor rise in the southern. In 
fact, Ave should thus have perpetual summer in the 
former, and perpetual Avinter in the latter ; and the 
same Avould be the case Avith the hemispheres to Avhich 
these zones appertain. 

But as the globe moA'es round its axis, move your 
hand sloAvly forward, so as to carry it from H 
toAvards E, and the boundary of light and darkness 
will approach toAvards the north pole, and recede from 
the south ; the nortiiern places Avill pass through less 
and less light, Avhile the southern will be more and 
more involved in it ; whence is shewn the decrease in 
the length of the days in the northern hemisphere, and 
the increase of the same in the southern. When the 
globe is at E, it is in a mean state betAveen the highest 
and loAvest points of its orbit ; the candle is directly 
over the equator, the boundary of light and darkness 
just reaches both the poles, and all places on the globe 
pass equally through the light and dark hemispheres, 
thereby shoAving tiiat the days and nights are then 
equal in all parts of the earth excepting only the poles, 
the sun there appearing as setting to the northern and 
rising to the southern. 

The globe being still moved forAvard, as it passes 
toAvards A, the north pole is more and more involved 
in the dark hemisphere, and the south pole advances 
more into the enlightened part ; till, Avhen it arrives 
at F, the candle is directly over the circle b b, and the 
days are then the shortest and the nights the longest 
throughout the northern hemisphere : and the reverse 
in the southern, the days there being the longest and 
the nights the shortest. The southern polar zone is 
now in perpetual light, and the northern in continual 
darkness. 

If the motion of the globe be still continued, as it 
moves through the quarter B, the north pole advances 
towards the light, and the south pole recedes from it ; 
the days lengthen in the northern hemisphere and 
shorten in the southern ; till, Avhen the globe arrives 
at G, the candle will be again over the equator (as 
when it Avas at E) ; the days and nights will be again 
equal in all parts of the earth ; the north pole Avill be 
just emerging out of darkness, and the southern pole 
beginning to be iuA^olved in it, as the northern pole 
Avas in the former instance Avhen the earth was at E. 

Hence is shoAvn the reason of the days lengthening 
and shortening from the equator to the polar circle 
every year, and why there is sometimes no day or 
no night for several revolutions of the earth within 
the two frigid zones ; and why there is but one day and 
one night in a year at the poles themselves. We see 
also that the days and nights at the equator are equal 
all the year round, this being always equally bisected 
by the circle bounding the light and darkness. 

A similar representation of these phenomena is ex- 
hibited in fig. 5 ; and in a subsequent chapter we shall Fig. 5. 



514 



ASTRONOMY. 



Astronomy, enter more particularly on the subject ; showing the 

^^— ^-v^«^ method of computing the length of the day in any 

given latitude ; and the time of the rising, setting, 

and southing of the sun on any proposed day, and in 

any given place. 

6. Of the Phases of the Moon. 

Phases of 32. The mooU;, of all the celestial bodies, is that which 
tlie moon, perhaps attracts most the attention, both of illiterate 
and scientific observers. The former class are drawn 
to their observations by the remarkable beauty and 
serenity of her light, her numerous changes or phases, 
the inconstancy of her illumination, the enjoyment of 
her light at certain seasons of the year, when the 
sun sinks early below the horizon, and the want of it 
when both luminaries rise and set at nearly the same 
hour. 

The philosophic observer examines her varying 
phases through his telescope ; sees the shadows of the 
hills on her surface projected to a considerable distance 
through plains and vallies, rendered by the power of 
optics nearly as distinct as those of a terrestrial plain 
at the distance of only a few miles ; he examines what 
he considers to be lunar volcanoes, and marks the 
progress of the lava from the crater to the vallies be- 
low ; he looks to determine some indication of erup- 
tions in present action ; endeavours to distinguish her 
seas and continents, to measure the heights of her 
mountains, and to ascertain the existence or non-ex- 
istence of a lunar atmosphere. 

Again, the practical astronomer is watching care- 
fully her deviating course in the heavens, and is 
endeavouring to submit her oscillating motion to the 
general principles of celestial mechanics ; and to con- 
struct formulae and tables, for the purpose of predict- 
ing her place at any appointed day and hour. 

These subjects Avill each engage our attention in the 
course of the following chapters of this treatise ; but 
at present we only propose to present to the reader an 
explanation of her most obvious phenomena, and to 
show their complete accordance with the motions and 
constitution of the solar system as described generally 
in the third chapter of this introduction. 
Phases of 33. The first lunar phenomena to which we shall call 
the moon, the readers' attention, is the continual change of 
figure, or the phases which she exhibits to a terres- 
trial spectator. At one time perfectly full or globular, 
at others half or a quarter illuminated, and at others 
again exhibiting only a fine arched line, barely 
perceptible to the naked eye. These appearances are 
doubtless due to the revolution of the moon in her 
orbit ; and the reflection of her light (which she re- 
ceives from the sun) towards the earth. The lunar 
globe is necessarily always one half illuminated as we 
have shown the earth to be in the last section ; and 
therefore, to a spectator placed in a line between the 
moon and sun, she would always present a full illu- 
minated circle or hemisphere ; but out of that line a 
greater or less part of the enlightened surface will be 
perceived, and which will obviously entirely vanish 
in certain positions. This may be illustrated by means 
of an ivory ball, as in the experiment described in the 
last section ; for the ball being held before a candle 
in various positions, will present a greater or less 
portion of the illuminated hemisphere to the view of 



the observer, according to his situation with regard 
to the illuminated axis. 

34. The same may be otherwise exhibited by means 
of our figure 6 ; where T is the earth, S the sun, and 
A, B, C, &c. the moon in diiferent parts of her orbit. 
When the moon is at A, in conjunction with the sim 
S, her dark hemisphere being entirely turned towards 
the earth, she will disappear as at a, there being no 
light on that side to render her visible. When she 
comes to her first octant at B, or has gone an eighth 
part of her orbit from her conjunction, a quarter of 
her enlightened side is towards the earth, and she ap- 
pears horned, as at b. When she has gone a quarter 
of her orbit from between the earth and sun to C, she 
shows us one half of her enliglitened side, as at c, and 
we say she is a quarter old. At D, she is in her second 
octant ; and by showing us more of her enlightened 
side she appears gibbous, as at d. At E, her whole 
enlightened side is towards the earth ; and therefore 
she appears round, as at e ; when we say it is full 
moon. In her third octant at F, part of her dark side 
being towards the earth, she again appears gibbous, 
and is on the decrease, as at/. At G, we see just one 
half of her enlightened side ; and she appears half 
decreased, or in her third quarter, as at g. At H, we 
only see a quarter of her enlightened side, being in 
her fourth octant ; where she appears horned, as at h. 
And at A, having completed her course from the sun 
to the sun again, she disappears ; and we say it is 
new moon. Thus, in going from A to E, the moon 
seems continually to increase ; and in going from E 
to A, to decrease in the same proportion ; having like 
phases at equal distances from A to E. But as seen 
from the sun S she is always full. 

The moon appears not perfectly round when she is 
full in the highest or lowest part of her orbit, because 
we ha^ e not a full view of her enlightened side at that 
time. When full in the highest point of her orbit, a 
small deficiency appears at her lower edge, and the 
contrary when full in the lower point of her orbit. 

35. The moon, as we have seen, shines by her reflected 
light ; in the same manner, the earth, by throwing 
back the light it receives from the sun, becomes in 
its turn a moon to the moon ; being full to the inha- 
bitants of the lunar sphere when our moon changes, 
and vice versa. For, when the moon is at A, new to 
the earth, the whole enlightened side of the earth is 
turned towards the moon ; and when the moon is at 
d, full to the earth, the dark side of the latter is 
turned towards the former. Hence a new moon an- 
swers to a full earth, and a full moon to a new earth. 
The quarters are also reversed with respect to each 
other. 

36. The position of the moon's cusps, or a right line 
touching the points of her horns, is very differently 
inclined to the horizon, at different hours of the same 
day of age. Sometimes she stands as it were upright 
on her lower horn, which is then necessarily perpendi- 
cular to the horizon ; when this happens, she is said 
to be in her nonagesimal degree, which is the highest 
point of the ecliptic above the horizon ; the ecliptic 
at that time being 90^ from each side of the horizon, 
reckoning from the point where it is then cut by 
the former circle. But this never happens when the 
moon is on the meridian, except when she is in the 
beginning of Cancer or Capricorn. 




Tlie earth 
is a moon ' 
to the 
moon. 



Position of 
the cusps of 
the moon. 



A S T R O N O M Y. 



5\i 



Astronomy. 37. Tlie moon turns on an axis which is nearly per- 
t _ , - 1^ -^ pendicular to the plane of the ecliptic, and in such a way 
The moon as to make one complete diurnal rotation during one 
always pre- lunation, and therefore always presents to us the same 
sents the ^,^^^ ^^. j^en^jgphere, as is demonstrable by observations 
to the earth, made on her by the telescope ; both these revolutions 
are performed in 27 days 7 hours 43', viz. from any 
star to the same star again, but from one lunation to 
another is about 29| days. In consequence of this re- 
markable coincidence, which is still unaccounted for 
on physical principles, the earth must appear to a spec- 
tator on the moon to be permanently at rest. It will 
never quit any position in which it is once found, at 
whatever height it may be above the lunar horizon, 
or in whatever quarter it may appear ; it will go 
through all its changes, but retain its position ; con- 
sequently to one half of the moon the earth is always 
invisible, while the other half enjoys a constant illu-' 
mination from its reflected rays ; but each side has 
en equd participation of the solar light. 
Phases of 33 'pj^g phases of the inferior planets. Mercury and 
le p anets. yenus, strongly resemble those of the moon, but they 
are invisible except by means of the telescope. Co- 
pernicus, after having laid down his system of celes- 
tial motions, predicted that future astronomers would 
find that Venus underwent the same changes, and ex- 
hibited similar phases to the moon ; which prediction 
was first fulfilled by Galileo, who directing his tele- 
scope to this planet, observed the phases foretold by 
-the father of modern astronomy ; he observed her to 
be sometimes full, sometimes horned, and sometimes 
gibbous. 

Mercury also presents similar appearances. All the 
difference being, that when these are full, the sun is 
between them and us, whereas, when the moon is full, 
we are between her and the sun. Mars appears some- 
times gibbous, but never horned, its orbit being ex- 
terior to that of the earth. 

We shall have again to recur to this subject, in a 
subsequent chapter, our purpose here being merely a 
popular illustration of the most striking lunar phe- 
nomena. 

7. Of lunar and solar eclipses. 
Of eclipses. 39. The phenomena of eclipses are amongst the num- 
ber of those w'hich have most engaged the attention 
of mankind ; the learned and the unlearned have found 
an equal interest in them ; the one to observe their 
appearances, to discover the cause of the deprivation 
of light which we then encounter, to predict their re- 
turn, &c. ; and we have seen, in our historical sketch, 
the various absurd ideas that haA^e been entertained on , 
this subject by many of the most eminent philosophers 
of antiquity. Amongst the common people, the interest 
excited by such phenomena, arose from the fear which 
they inspired ; they were considered by them as 
alarming deviations from the regular course of nature, 
and as the forerunners of some portentous event : 
hence, actuated either by curiosity or timidity, the 
subject of eclipses has probably from the earliest times 
engaged the serious attention of mankind, and they 
are still amongst the most interesting of the celestial 
phenomena. In illustrating the cause of eclipses, we 
shall follow still the method we have hitherto pursued 
in this introduction ; that is, we shall render our ex- 
planation as popular and simple as possible, leaving 



all the minute particulars for anotlier place, where Ave Plane 
shall enter more fully upon the subject, and illustrate Astronomy, 
the principles of those calculations on Avhich the pre- ^"V"' 
diction of eclipses depends. 

40. The eartli being an opaque body enlightened by Eclipse of 
the sun, it necessarily projects a shadoAv into the regions tl'e moon, 
of space in a contrary direction ; and Avlien it so hap- 
pens that the moon in the course of her revolution 
about the earth, falls into this shadoAV, she loses the 
sun's light by which alone she is A'isible, and appears 
to us eclipsed. Let us suppose two straight lines 
draAvn from the opposite pans of the solar disc tan- 
gents to the surface of the earth as AB, a b, (fig. 7) Fig. 7. 
these lines will represent the limits of the shadoAv, 
and as the sun is much larger than the earth, these 
lines Avill meet at a point, and cross each other behind 
the earth ; and the shadoAv Avill thus assume the figure 
of a right cone. When the moon enters this shadoAv, 
and a part of her disc is still enlightened by the sun, 
this part is not terminated by a straight line, but has 
the form of a luminous crescent, the concave part 
being turned tOAvards the shade. The same circum- 
stance happens again, when the moon begins to quit 
the shadow. 

Wlien the moon approaches the terrestrial shadoAv, 
she does not lose her light suddenly, but it gradually 
becomes more and more faint till the obscurity arrives 
at its greatest intensity. In order the better to com- 
prehend this phenomenon, we have only to attend to 
tiie figure, and observe, that an opaque body may be 
so placed betAveen an object and the sun as only to 
intercept a part of its light ; let us suppose this object 
to be M, it will then be less illuminated than if it re- 
ceived the whole of the light, but more of it than if 
it were placed at m in total obscurity. 

41. This intermediate state comprehended between pgj,mv,iL 
the angular space EBC on one side of the umbra or 
shadoAV, and FBC on the other, is called the penumbra; 
and it is the entrance of the moon into this partial 
shade, Avhich produces the faint obscurity observed 
immediately before the eclipse commences, and after 
it is over. 

The limits of this penumbra may be found by draAV- 
ing tAvo lines as A e, a E touching the surface of the 
sun and the earth, so as to cross at a point C betAA^een 
them. The angles EBC, ebc Avill determine the space 
occupied by the penumbra ; for at a point situated 
beyond this space, the whole disc of the sun Avill be 
visible, and the visible portion will diminish from the 
line EB to CB, Avheu it Avill entirely disappear, and 
consequently the penumbra AA'ill gradually increase in 
its intensity from its first limit EB, to its second BC, 
where it ceases, or is confounded Avith the shadoAv itself. 

42. When the moon enters completely into the sha- p^jnj; jj^j^j 
dow of the earth, Ave still do not entirely lose sight of it ; observed in 
its surface is still faintly illuminated AA'ith a reddish atot.illunar 
light, something similar to that reflected by the eclipse, 
clouds after the setting of the sun. This effect arises 
from the solar rays that have been refracted by our 
atmosphere, and afterAvards inflected behind i\\e earth ; 
for those rays Avhich are not enough refracted to reach 
the surface of the earth, continue their course through 
the atmosphere, and if not entirely absorbed by it, 
are inflected tOAvards a focus or point in the same 
manner as in a convex lens. 

The light thus refracted behiud the earth is very 



516 



ASTRONOMY. 



Solar 
eclipse. 



Fig, 



Astronomy, considerable : regarding only one luminous point 
■s— -y-—^ of the solar disc, it can only project one ray to eVery 
point of the surrounding space, but through the me- 
dium of the terrestrial atmosphere, a course of lumi- 
nous points is collected behind the earth, an object 
placed in the focus or vertex of this cone, woiild be 
more strongly illuminated than by the direct light of 
the sun ; every point of the sun producing a similar 
effect, the length and extension of the terrestrial sha- 
dow are much diminished ; and if the atmosphere did 
not absorb a very great portion of the solar rays, the 
light reflected from the disc of the moon would be 
very great ; it is, however, so much modified by the 
circumstances alluded to, as to exhibit only that 
faint red light above described. 

It may be proper to observe, that this faint illumi- 
nation of the lunar disc at the time of a total eclipse,. 
has been accounted for upon different principles, but 
the above appears to us the most satisfactory. 

43. An eclipse of the sun is an occultation of the sun's 
body, occasioned by the interposition of the moon be- 
tween the earth and sun. On this account it is by 
some considered rather as an eclipse of the earth, be- 
cause the light of the sun is hidden from the earth by 
the moon, whose shadow involves a part of the terres- 
trial surface. The cause of a solar eclipse, and the 
circumstances attending it are represented in fig. 8, 
where S is the sun, m the moon, and CD the earth, 
rniso the moon's conical shadow traversing a part 
of the earth CoD, and thus producing an eclipse to 
all the inhabitants residing in that track, but no where 
else ; excepting that for a large space around it, there 
is a fainter shade included within all the space rCDs, 
which, as in the lunar eclipse, is called the pe- 
numbra. 

Hence, solar eclipses happen when the moon and 
sun are in conjunction, whereas the lunar eclipses only 
take place when they are in opposition ; that is, the 
former happen at the time of the new moon, and the 
latter at the full. 

44. Notwithstanding the moon is very considerably 
less than the sun, yet from its proximity to us, it so hap- 
pens, that its apparent diameter differs very little from 
that of the latter body, and even sometimes exceeds 
it. Suppose an observer situated in a right line which 
joins the continuation of the sun and moon, he will 
see the former of these bodies eclipsed^ as we have 
above stated. If the apparent diameter surpasses that 
of the sun, the eclipse will be total, and the observer 
will be entirely immerged in the conical shadow which 
is projected behind the moon : if the diameters are 
equal, the point of the cone will terminate at the 
earth's surface, and there will be a momentary total 
eclipse. If the diameter of the moon be less than that 
of the sun, the observer will see a zone of the sun 
surrounding the moon like a ring, and the eclipse 
will be central and annular. And lastly, if the obser- 
ver be not exactly in the line joining the centres, the 
eclipse may be partial ; that is, a part of the solar disc 
may be hid while the remaining part continues per- 
fectly visible. Total eclipses, which are very rare 
occurrences in any particular place, are remarkable 
for the darkness which accompanies them, and which 
they spread over different parts of the surface of the 
earth, in the same manner as the shadow of a dense 
cloud, carried along by the wind, sweeps over the 



Different 
Jiiud. 



Partial. 



mountains and the plains, depriving them for some Plane 
instants of the light of the sun. This total darkness Astronomy, 
under the most favourable circumstances may last '^— v—^^ 
about five minutes. The smallest apparent diameter 
of the sun is SV ZO" ; the diameter of the moon at 
its mean distance 31' 25'', that is less than that of the 
sun ; consequently there cannot be a total eclipse 
when the moon is beyond its mean distance. Eclipses 
of the sun are also modified as to quantity by the 
height of the moon above the horizon which increases 
her diameter ; other circumstances also contribute to 
produce certain changes which must be considered in 
the computations relative to these phenomena, but 
which it would be useless to detail in this place. 
From what has been already stated we may draw the 
following general conclusions. 

1. That no solar eclipse is universal j that is, none General de- 
can be visible to the whole hemisphere to which the Auctions, 
sun is risen : the moon's disc being too small and 

too near the earth to hide the sun from a whole ter- 
restrial hemisphere. Commonly, the moon's dark 
shadow covers only a spot on the earth's surface, 
about ISO miles broad, when the sun's distance is 
greatest, and the moon's least. But her partial sha- 
dow or penumbra, may then cover a circular space of 
4,900 miles in diameter, within which the sun is more 
or less eclipsed, as the places are nearer to or farther 
from the centre of the penumbra. In this case, the 
axis of the shade passes through the centre of the 
earth, or the new moon happens exactly in the node, 
and then it is evident that the section of the shadow is 
circular ; but in every other case the conical sha- 
dow is cut obliquely by the surface of the earth, and 
the section will be oval, and very nearly a true ellipsis, 

2. Nor does the eclipse appear the same in all parts 
of the earth, where it is seen ; but when in one place it 
is total, in another it is only partial. Moreover, 
when the apparent diameter of the moon is less than 
that of the sun, as happens when the former is in apo- 
gee and the latter in perigee, the lunar shadow is then 
too short to reach the earth's surface ; in which case, 
although the conjunction be central, yet the sun will 
be to no place totally eclipsed, but to certain observers, 
a bright rim of light will be seen surrounding the 
moon while the latter is on the solar disc; and the 
eclipse is then said to be annular. 

3. A solar eclipse does not happen at the same time 
in all places where it is seen ; but appears earlier to 
the western parts, and later to the eastern ; as the 
motion of the moon, and consequently of her shadow, 
is from east to west. 

4. Inmost solar eclipses, the moon's disc is covered 
with a faint light ; which is attributed to the reflec- 
tion of the rays from the illuminated part of the 
earth. 

Lastly. In total eclipses of the sun, the moon's 
limb is seen surrounded by a pale circle of light, 
which has been considered as indicative of a lunar 
atmosphere ; others, however, doubt this explana- 
tion, and offer diff'erent conjectures as to the cause of 
the phenomenon ; but this is not the place for dis- 
cussing this question. 

Having thus given a brief description of the consti- 
tution of the solar system, with an illustration of the 
most remarkable phenomena which it presents to 
naked vision, as far as they can be illustrated inde-> 



ASTRONOMY. 



517 



Astronomy, pendent of astronomical computation, we shall now 
*— V-»^ conclude our introduction by describing certain astro- 
nomical machines, constructed for the purpose of ex- 
hibiting, in a simple and popular manner, all the most 
remarkable celestial movements and phenomena. 

8. Description of astronomical machines. 
Astronomi- ■^^- ^Y astronomical machines is here to be under- 
cal ma- Stood any piecesof mechanism constructed for exhibiting 
chines. the motions and phenomena of the heavenly bodies, be- 
ing thus distinguished from astronomical instruments, 
Avhich include all such constructions as are employed 
for the purpose of measuring altitudes, angles, &c. 
necessary for astronomical computation. The one, in 
fact, are merely employed for explanation ; the other, 
for the purpose of research and calculation. Various 
improvements have been made by different artists in 
the construction of planetary machines, and that which 
is now exhibited in the lectures of the Royal Institu- 
tion, is perhaps the most perfect of its kind ; but it 
would carry us too far to describe this instrument, 
with all its apparatus, wheel work, &c. Beside, we 
cannot help observing, that much time, ingenuity, and 
expence are frequently wasted in these kind of con- 
structions ; because, after all, they are only, as we 
have before observed, explanatory ; for which purpose 
the same degree of accuracy is not required as in in- 
struments employed in astronomical observation. 
That student who stands in need of the assistance 
of such machines, wiU never become a great profi- 
cient in astronomy ; to pursue this study Avith effect, 
a beginner must acquire the habit of constructing his 
own planetarium in his mind's eye, and of soaring 
with it into the regions of celestial space ; he ought 
to conceive the orbits of the heavenly bodies in a free 
non-resisting medium, their nodes, their inclinations, 
and eccentricities unimpeded by the intervention of 
brass rings or ebony frames ; which have always the 
effect of giving a stiffness and unnatural representa- 
tion extremely offensive to the eye of the professed 
astronomer. We must, however, acknowledge, that 
to children or mere novices, these machines may be 
of some assistance, and shall therefore describe one or 
two of the most simple of them in this place. 

Planetarium. 
Planeta- 46. The machine exhibited in fig. 9, is a planetarium, 

rium, by constructed by the late Mr. Jones, of Holborn. It 
Jones. represents, in a general manner, by various parts of it, 

^^' ^' all the principal motions and phenomena of the hea- 
venly bodies. 

The sun occupies the centre, with the planets Mer- 
cury, Venus, the Earth with its moon. Mars, Jupiter, 
with his four satellites, Saturn with his seven, and an 
occasional long arm may be attached for exhibiting 
the Herschel or Uranus, with his several attendants. 
To the earth and moon is applied a frame, CD, con- 
taining only four wheels and two pinions, which serve 
to preserve the earth's axis in its proper parallelism 
in its motion round the svui, and to give the moon her 
due revolution round the earth at the same time. 
These wheels are connected with the wheel work in 
the round box below, and the whole is set in motion 
by the winch H. The arm M that carries round the 
moon, points out on the plate C her age and phases 
for any situation in her orbit, which are engraved 



upon it. In the same manner, the arm points out her pj^ng 
place in the ecliptic B, in signs and degrees, called Astronomy, 
her geocentric place ; that is, as seen from the earth, "s— -^-^^^ 
The moon's orbit is represented by the flat rim A ; 
this orbit is made to incline to any desired angle. 
The earth of tliis instrument is usually made of a 3- 
inch, or l|-inch globe, papered, &c. for the purpose ; 
and by means of the terminating wire, that goes over 
it, points out the changes of the seasons, and the dif- 
ferent length of days and nights. It may also be made 
to represent the Ptolemaic system, which places the 
earth in the centre, and the planets and sun revolving 
about it. This is done by an auxiliary small sun and 
earth, which change their places in the instrument j p e f. .• 
but at the same time it affords a most manifest con- ^f ptole- 
futation of it. For it is obviously perceived in this male sys- 
construction, first, that the planets Mercury and Ve- tem. 
nus being both witliin the orbit of the sun, cannot at 
any time be seen to go behind it, whereas, in nature, 
we see them as often go behind as before the sun in 
the heavens. It shows that as the planets move in 
circular orbits about the central earth, they ought at 
all times to be of the same apparent magnitude ; 
whereas, on the contrary, we observe their apparent 
magnitude in the heavens to be very variable ; and 
so far different, that Mars, for instance, will some- 
times appear nearly as large as Jupiter ; while, at 
others, he will scarcely be distinguishable from a fixed 
star. 

The planetarium, when thus adjusted, shows also 
that the motions of the planets ought always to be 
regular and uniform ; that they ought always to 
move in the same direction ; whereas, we find them, 
sometimes direct, at others stationary, and even retro- 
grade ; which plainly shows the fallacy of the Ptole- 
maic hypothesis, at the same time that the modern 
system is thus clearly represented. Let us, for ex- 
ample, take the earth from the centre, and replacing 
it by the ball representing the sun, also restoring the 
earth to its proper situation amongst the planets, and 
every phenomena will then correspond and agree ex- 
actly with celestial observations. For turning the 
handle H, we shall see the planets Mercury and Ve- 
nus go both before and behind the sun, or have two 
conjunctions ; we shall perceive also that Mercury 
can never have more than a certain angular distance 
21° from that body, nor Venus a greater than 47°. 
It will likewise be seen, that the superior planets, par- 
ticularly Mars, will sometimes be much nearer to the 
earth than at others ; and, consequently, must vary 
considerably in their apparent magnitude ; we shall see 
that these planets cannot appear from the earth to 
move with equal velocities ; but that this wiU appear 
greater when they are nearest, and less as they are 
more remote ; that their apparent motions ouglit 
sometimes to be direct, sometimes retrograde, while 
in particular positions they will seem to be stationary ; 
all which are consistent with the actually observed 
phenomena. 

These particulars are shown somewhat more mi- 
nutely in fig. 10, where a hollow wire, with a slit at Tig, 10. 
top, is placed over the arm of the planet Mercury or 
Venus, at E. The arm DG represents a ray of light 
proceeding from the planet at D to the earth, and is 
put over the centre which carries the earth at F. The 
machine being then put in motion, the planet D, as 
3x 



518 



ASTRONOMY. 



Astronomy, seen in the heavens from the earth at F, will unclerg;o 
v«.— y-^^ the several changes of position as above described ; 
and a similar application may be made to the superior 
planets. 

This apparatus serves also to illustrate the diurnal 
rotation of the earth on its axis ; the cause of the 
different seasons, the difference in the lengths of the 
days and nights, &c. For as the earth is placed on 
an axis inclined to the plane of the ecliptic at an angle 
of 23§°, we shall have, when the machine is in motion, 
the most satisfactory illustration of the different in- 
clination of the sun's rays upon the earth. The dif- 
ferent quantities which fall on a given space, the 
unequal quantities of the atmosphere they pass 
through, and the unequal duration of the sun above 
the horizon at the same place at different times of the 
year ; which circumstances constitute the primary 
causes of all that change of seasons and variable 
lengths of days and nights which we experience. 

The globe representing the earth being moveable 
about an axis, if we draw upon it a circle to denote 
our own horizon, we may, by means of the terminat- 
ing wire going over it, very naturally exhibit the 
cause of the different lengths of the days and nights 
in our particular latitude, by simply turning the arti- 
ficial earth with the hand to imitate its diurnal rota- 
tion ; but in some of the more modern instruments of 
this kind, this rotatory motion is communicated to 
the globe by the wheel work of the machine itself. 

The eclipses of the sun and moon are still more 
perfectly shown by this machine than the phenomena 
to which we have above alluded ; for by placmg a 
light in the centre instead of the brass ball, denoting 
Fig. 11. the sun (fig. 11), and turning the handle till the 
moon comes into a riglit line, between the centres of 
the light, or sun, and the earth, the shadow of the 
moon will fall upon the latter, and all the inhabitants 
of those parts over which the shadow passes, will see 
more or less of the eclipse ; and on the other side the 
moon passes through the shadow of the earth, and is 
by that means eclipsed to the inhabitants of those 
parts to which the lunar disc is at that time visible. 

All the phenomena of the satellites of Jupiter, 
Saturn, &c., might also, with equal facilities, be ex- 
hibited by this machine, and are actually so exhibited 
in some of the larger apparatus, denominated orreries ; 
in the machine we are at present describing, these 
satellites are only moveable by hand. 

Orreries. 
Of the Or- 47. The term Orrery, to denote such a machine as that 
rery. we are about to describe, appears rather singular, and 

is one of those derivations, which, if the history were 
lost, would involve future etymologists in inexplicable 
difficulties. The first machine of this kind appears to 
have been made by the celebrated instrument maker, 
Graham, by whom it was probably considered only 
as an improved planetarium : but Rowley, an artist 
of reputation in his time, copied Graham's machine, 
and the first of his construction was made for the Earl 
of Orrery ; whence Sir R. Steel, who knew nothing 
of Graham's original claim, called the instrument 
after the name of the supposed first purchaser an 
Orrery, which designation it still bears. One of the 
most usual constructions of this kind is shown in 
Rg. 12. (fig. 12,) which may be briefly described as follows :•— 



The frame of it, which contains the wheel work, piane 
&c. and regulates the whole machine, is made of Astronomy, 
ebony, and about four feet in diameter. Above the ^— -y-^*' 
frame is a broad ring supported by twelve pillars, 
which ring represents the plane of the ecliptic. Upon 
it are two circles divided into degrees with the names 
and characters of the twelve signs of the zodiac. Near 
the outside is a circle of months and days, exactly 
corresponding to the sun's place at noon each day 
throughout the year. Above the ecliptic stand some 
of the principal circles of the sphere corresponding 
with their respective situations in the heavens ; viz. a a 
are the two colures, divided into degrees and half de- 
grees ; b is one half of the equinoctial circle, making 
an angle of 23^ degrees with the ecliptic. The tropic 
of Cancer and the arctic circle are each fixed parallel 
at their proper distances from the equinoctial. On 
the northern half of the ecliptic is a brass semicircle 
moveable upon two fixed points in t and ih . 

This semicircle serves as a moveable horizon, to be 
put to any degree of latitude on the north part of the 
meridian, and the whole machine may be set to any 
latitude, without disturbing any of the internal mo- 
tions, by means of two strong hinges fixed to the bot- 
tom frame upon which the instrument moves, and a 
strong brass arch, having holes at every degree, 
through which a pin may he passed at any required 
elevation. These hinges, with the arch, support the 
whole machine when set to the proposed latitude. 

"When the Orrery is thus adjusted, set the move- 
able horizon to any degree upon the meridian, whence 
may be formed a pretty correct idea of the respective 
altitude or depressions of the several planets, both 
primary' and secondary. The sun S stands in the 
centre of the system on a v.ire making an angle with 
the ecliptic of about 82° ; next in their order follow 
the planets Mercury, Venus, and the Earth, the axis 
of the latter being inclined to the plane of the ecliptic, 
at an angle of 66^^, which is the measure of the in- 
clination of the earth's axis. 

Near the bottom of this axis is a dial plate, having 
an index pointing to the hours of the day, as the Earth 
revolves ; and about the latter is a small ring, sup- 
ported by two small pillars, representing the orbit of 
the moon, with divisions answering to the moon's 
latitude. The motion of this ring represents the 
motion of the lunar orbit according to that of the 
nodes ; and within it is a small ball with a black cup, 
or case, by which are exliibited all the phases of this 
celestial body. 

Beyond the orbit of the earth are those of Mars, 
Jupiter, and Saturn, and in some instruments the 
Georgium Sidus, or Uranus. Jupiter is attended by 
his four satellites, and Saturn by his seven satellites 
and ring. 

The machine is put in motion by turning a handle, 
or winch ; and by pushing in, and pulling out a small 
pin above the handle. When it is in, all the planets, 
both primary and secondary, will move according to 
their respective periods. When it is out, the motion 
of the satellites of Jupiter and Saturn are stopped, 
while all the rest move without interruption. 'There 
is also a brass lamp, having two convex glasses to 
put in the place of the sun ; and also a smaller earth 
and moon made somewhat in proportion to their dis- 
tance from each other, and which may be put on or 



ASTRONOMY. 



519 



Astronomy, removed at pleasure. The lamp turns round at the 
^ _.- ^' same time with the earth, and the glasses of it cast a 
■ strong' light upon her. When it is intended to use 
the. machine, the planets must be first placed each in 
its respective position by means of an astronomical 
ephemeris, and a black patch or wafer may be placed 
on the middle of the sun ; against the first degree of 
T (Aries) ; patches may also be placed upon Venus, 
Mars, and Jupiter. Now turn the handle, one revo- 
lution of which corresponds to one diurnal revolution of 
the earth about its axis, and consequently answers to 
24 hours upon the dial plate, placed at the foot of the 
wire on which the ball is fixed. 

Again, when the index has moved over the space 
of 10 hours, Jupiter will have made one revolution on 
his axis, and so of the rest according to their respec- 
tive periods of diurnal rotation. By these means the 
revolution of the planets, and their motion round 
their axis, will be represented to the eye, if not ex- 
actly, yet in nearly their due intervals of time. 

48. We might have entered into the description of 
orreries on other and more correct principles than the 
above, but the explanation must have been propor- 
tionally longer ; and we have already observed, that 
such machines are, in our opinion, rather calculated to 
show the ingenuity of tlieir constructors, than to offer 
any advantages to the student. It is true, that they 
may convey to the uninformed reader some ideas of 
the planetary motions, but we think it is extremely 
probable, that the idea thus given, if not actually 
false, may, in many cases, be rather injurious than 
useful ; and as instruments for computation, the 
most perfect of them are wholly incompetent, we 
shall therefore make no apology for not having ex- 
tended our description of orreries to a greater length. 
What has been said, and a reference to the plate, will 
be quite sufficient for showing the general principle 
of their construction and operation, which, we con- 
ceive, is all that is requisite to be introduced in this 
place. 

Cometarium. 

Cometa- ^9. This machine,which must also be considered rather 
rium. as an object of curiosity than utility, shows the motion 

of a comet, or very eccentric body, moving i-ound the 
sun, and describing equal areas in equal times j and 
may be so adjusted, as to show such a motion for any 
degree of eccentricity. The first projection of it we 
owe to Desaguliers. 
Fig. 13, 14. The dark elliptical groove, abed &c. (fig. 13,) 
is the orbit of the comet Y ; which is carried round 
in this groove according to the order of tliose letters, 
by the wire W fixed to the sun S, and slides on the 
wire as it approaches nearer or recedes further from, 
the sun ; being nearest, or in its perihelion in a, and 
most distant in the aphelion g. The areas aS b, 6 S c, 
cSd, &c. or the contents of these several trilaterals, are 
all equal ; and in every turn of the winch, or handle, 
N, the comet Y is carried over one of these spaces ; 
consequently, in the same time as it moves from /to 
g, or from g to h, it will also move from m to a, or 
from a to 6, and so of the rest, its motion being quick- 
est at a, and slowest at g. Thus the comet's velocity 
in its orbit continually decreases from the perihelion 
to the aphelion, and increases in the same proportion 
from g to a. 



The ecliptic orbit is divided into 12 equal parts or Plane 
signs, with their respective degrees, as is also the Astronomy, 
circle n o p q, &c., which represents a great circle ^^—"V*^ 
in the heavens, and to which the comet's motion is 
referred by a small knob on the point of the wire W. 
While the comet moves from / to g- in its orbit, it 
appears to move only about five degrees in this circle, 
as is shown by the small knob on the end of the wire 
W ; but in as short a time as the comet moves from 
m to a, or from a to b, it appears to describe the large 
space in the heavens t n, or n o, either of which spaces 
contains 120°, or four signs. If the eccentricity of 
the orbit were greater, the greater also would be 
the difference in the cometary motion. 

The circular orbit ABC, &c. is for showing the 
equable motion of a body about the sun S, describing 
equal areas in equal times, with those of a body Y in 
its elliptic orbit above referred to, but with this differ- 
ence, that the circular areas ASB, BSC, &c. or the 
equal arcs AB, BC, &c. are described in the same 
times as the unequal elliptic arcs a b, b c, &c. 

If we conceive the two bodies Y and R, to move 
from the points a, A, at the same moment of time, 
and each to go round its respective orbit, and to 
arrive at the same points again at the same instant, the 
body Y will be more forward in its orbit than the body 
R all the way from a to g, and from A to G : but R 
will be forwarder than Y through all the other half 
of the orbit ; and the difference is equal to the equa- 
tion of the body Y in its orbit. At the points a A, 
and g G, that is, in the perihelion and aphelion they 
will be equal ; and then the equation vanishes. This 
shows why the equation of a body moving in an ellip- 
tic orbit, is added to the mean or supposed circiilar 
motion from the perihelion to the aphelion, and sub- 
tracted from the aphelion to the perihelion, in bodies 
moving round the sun, or from the perigee to the 
apogee, and from the apogee to the perigee in the 
moon's motion round the earth. 

This motion is performed in the following manner 
by the machine, (fig. 15.) ABC is a wooden bar (in Fig. 15. 
the box containing the wheel-work), above which are 
the wheels D and E, and below it the elliptic plates 
FF and GG ; each plate being fixed on an axis in one 
of its foci, at E and K ; and the wheel E is fixed 
on the same axis with the plate FF. These plates 
have grooves round their edges precisely of equal 
diameters to one another, and in these grooves is the 
cat-gut string g g, g g crossing between the plates at 
h. On H, tlie axis of the handle or winch N in fig. 
13, is an endless screw in fig. 15, working in the 
wheels D and E, whose numbers of teeth being equal, 
and equal to the number of lines a S, b B, cS, &c. in 
fig. 14, they turn round their axis in equal times to 
one another, as do likewise the elliptic plates. For, 
the wheels D and E having equal numbers of teeth, 
the plate FF being fixed on the same axis with the 
wheel E, and turning the plate GG of equal size by a 
cat-gut string round them both, they must all go 
round their axis in as many turns of the handle N as 
either of the wheels has teeth. 

It is easy to see, that the end h of the elliptical 
plate FF being farther from its axis E than the oppo- 
site end I is, must describe a circle so much the larger 
in proportion, and must therefore move through so 
much more space in the same time^ and for that 
3x3 



520 



ASTRONOMY. 



Astronomy, reason the end h moves so much faster than the end 
^^--V-»^ I, although it goes no sooner round the centre E : at 
the same time the quick-moving end Ii of the plate 
FF leads about the short end h K of the plate GG with 
the same velocity ; and the slow-moving end 1 of the 
plate FF coming half round as to B, must then lead 
the long end k of the plate GG about, with a corres- 
ponding slow motion : so that the elliptical plate FF 
and its axis E move uniformly and equally quick in 
every part of its revolution ; but the elliptical plate 
GG, together with its axis K, must move very une- 
qually in different parts of its revolution ; the differ- 
ence being always inversely as the distance of any 
point of the circumference of GG from its axis at K j 
or in other words, if the distance K k, be four, five, or 
six times as great as the distance K h, the point /i will 
move in that position, four, five, or six times as fast 
as the point k does when the plate GG has gone half 
round ; and so on for any other eccentricity or differ- 
ence of the distances K k, K h. Ihe I on the plate 
EF, falls in between the two teeth at k on the plate 
GG ; by which means the revolution of the latter is 
adjusted to that of the former^ so that they can never 
vary the one from the other. 

On the top of the axis of the equally moving wheel 
D (fig. 15) is the sun S (fig. 14) which by means of 
the wire attached to it, carries the ball R round the 
circle, ABC, &c. with an equable motion, according 
to the order of the letters ; and on the top of the axis 
K of the unequally moving ellipse GG in (fig. 15) is 
the sun S (fig. 14) carrying the ball Y unequally 
round the elliptic groove abed, &c. Avhich elliptic 
groove must be exactly equal and similar to the verge 
of the plate GG, which again is also equal to that of 
EF. 



Eclipsarean 50. The eclipsarean is aninstrnment invented by Mr. 
Ferguson for exhibiting the time, quantity, duration, 
and progress of solar eclipses, in all parts of the earth. 
This machine consists of a terrestrial globe A, (fig. 

Tig. 16,17. 17) turned by a winch M, round its axis B, inclining 
23^°, and carrying an index round the hour circle D; 
a circular plate E, on which the months and days of 
the year are inserted, and which supports the globe 
in such a manner, that when the given day of the 
month is turned to the annual index G, the axis has 
the same position with the earth's axis at that time ; 
a crooked wire F, which points to the middle of the 
earth's enlightened disc, and shows to what place of 
the earth the sun is vertical at any given time ; a 
penumbra or thin circular plate of brass I, divided 
into twelve digits by twelve concentric circles and so 
proportioned to the size of the globe, that its shadow, 
formed by the sun, or a candle, placed at a convenient 
distance, with its rays transmitted through a convex 
lens, to make them fall parallel on the globe, may 
cover those parts of the globe which the shadow and 
penumbra of the moon cover on the earth ; an up- 
right frame HHHH, on the sides of which are scales 
of the moon's latitude, with two sliders K and K, 
fitted to them, by means of which the centre of the 
penumbra may be always adjusted to the moon's lati- 
tude ; a solar horizon C, dividing the enlightened 
from the darkened hemisphere, and showing the places 
where the general eclipse begins and ends with the 



rising or setting sun, and a handle M, which turns Plane 
the globe round its axis by the wheel work, and Astronomy '. 
moves the penumbra across the frames by threads '^—'^'^'^ 
over the pulleys LLL, with a velocity duly propor- 
tioned to that of the moon's shadow over the earth 
as the earth turns round its axis. 

51. If the moon's latitude at any conjunction exceeds Rectlfica- 
the number of divisions on the scales, there can be no tion. 
eclipse ; if not, the sun wiU be eclipsed to some parts of 

the earth ; the appearance of which may be represented 
by the machine, either with the light of the sun, or of 
a candle. For this purpose, let the indexes of the sli-^ 
ders KK, point to the moon's latitude, and let the plate 
E be turned till the day of the given new moon comes 
to G, and the penumbra be moved till its centre comes 
to the perpendicular thread in the middle of the 
frame, which thread represents the axis of the eclip- 
tic ; then turn the handle till the meridian of London 
on the globe comes under the point of the wire F, 
and turn the hour circle D till 12 at noon comes to 
its index ; also turn the handle till the hour index 
points to the time of new moon in the circle D, and 
then screw fast the collar N. Lastly, elevate the ma- 
chine till the sun shines through the sight holes in 
the small upright plates OO, on the pedestal, or 
place a candle before the machine, at the distance of 
about four yards, so that the shadow of the intersec- 
tion of the cross thread in the middle of the frame, 
may fall precisely on that part of the globe to which 
the wire F points ; with a pair of compasses take the 
distance between the centre of the penumbra and the 
intersection of the threads, and set the candle higher 
or lower, according to that distance ; and place a 
large convex lens between the machine and candle, 
so that the candle may be in the focus of the lens } 
and thus the machine is rectified for use. 

52. Let the candle be turned backward till the pe- Phenomena 

numbra almost touches the side, HF, of the frame, sbown by 

and then turning it forward, the following phenomena H'? ™^" 

. , J ° ^ chine, 

may be observed. 

1. Where the eastern edge of the shadow of the 
penumbral plate I, first touches the globe at the solar 
horizon, those who inhabit the corresponding part of 
the earth, see the eclipse begin on the uppermost 
edge of the sun, just at the time of its rising. 

2. In that place where the penumbra's centre first 
touches the globe, the inhabitants have the sun rising 
upon them centrally eclipsed. 

3. When the whole penumbra just falls upon the 
globe, its western edge at the solar horizon touches, 
and leaves the place where the eclipse ends at sunrise 
on his lowermost edge. 

4. By continued turning, the cross lines in the cen- 
tre of the penumbra will go over all those places on 
the globe where the sun is centrally eclipsed. 

5. When the eastern edge of the shadow touches 
any place of the globe, the eclipse begins there ; when 
the vertical line in the penumbra comes to any place, 
then is the greatest obscuration at that place ; and 
when the western edge of the penumbra leaves the 
place, the eclipse ends there, and the times are shown 
on the hour circle ; and from the beginning to the 
end, the shadows of the concentric penumbral circles 
show the number of digits eclipsed at all the interme- 
diate times. 

6. When the eastern edge of the penumbra leaves 



ASTRONOM Y. 



521 



Astronomy, tjjg globe at the solar horizon C, the inhabitants see 
^""~v-~"^ the sun beginning to be eclipsed on its lowermost 
edge, at its setting. 

7. Where the centre of the penumbra leaves the 
globe, the inhabitants see the sun centrally eclipsed; and 
lastly, where the penumbra is wholly departing from 
the globe, the inhabitants see the eclipse ending on 
the uppermost part of the sun's edge, at the time of 
its disappearing in the horizon. 

This instrument will likewise serve for exhibiting 
the time of sun rising and setting; and of morning 
and evening twilight, as well as the places to which 
the sun is vertical on any day, by setting the day on 
the plate E to the index G, turning the handle till the 
meridian of the place comes under the point of the 
crooked wire F, and bringing XII on the hour circle 
D to the index : then if the globe be turned till the 
place touches the eastern edge of the horizon C, the 
index shows the time of sun setting ; and when the 
place comes out from below the other edge of C, the 
index shows the time when evening t^vilight ends ; 
morning twilight and sun rising are shown in the 
same manner on the other side of the globe. And 
the places under the point of the wire F are those to 
which the sun passes vertically on that day. Fergu- 
■lon's Astronomy, by Brewster, or Phil. Trans, vol. 
xlviii. 

53. The celestial atid terrestrial globes may also be 
considered as astronomical machines of the kind we 
have been describing ; but it would too much inter- 
rupt the order of our treatise to enter upon a descrip- 
tion of these instruments in this place ; they will, 
therefore be described under the proper head in our 
alphabetical arrangement ; and we shall now proceed, 
having given the foregoing succinct view of the more 
popular celestial phenomena, to treat the subject un- 
der a more scientific point of view, in the following 
sections. 

PART II. 

PLANE ASTRONOMY, 

§ III. Containing the principles of astronomical com- 
putation. 

1. Definitions. 

Of the ^■*- I'revious to our entering upon this subject, it 

Bpliere de- "will be requisite for the reader to render himself familiar 

finitions. with the following definitions. Some of them have 

been already given, but the convenience of having one 

decided place of reference will compensate for the few 

repetitions that occur. 

Agreatclr- 1. A great circle of a sphere is any circle QRST (fig. 

^f- 18) whose plane passes through the centre of the 

'^' ■ sphere ; and a small circle is any circle, BHK, Avhose 

plane does not pass through the centre. All great 

circles bisect each other. 

A diameter 2. The diameter of a sphere is any line, PE, passing 

through the centre and terminated on both sides by 

the circumference ; this diameter is said to be the 

axis of that great circle to which it is perpendicular ; 

and the extremity of the axis PE are called the poles 

of that circle. 

Hence it follows, that the pole of a great circle is 90" 
distant from every point of it upon the sphere ; and 
that the arcs subtending any angles at the centre of a 



sphere are those of great circles. Consequently, aU Plane 
the triangles formed on the surface of a sphere for the Astronomjr 
solution of spherical problems must be formed by the ^"""v^'*^ 
arcs of groat circles. 

3. Secondaries to a great circle are great circles, as Seconda- 
PQE, PRE, which pass through its poles, and whose "cs. 
planes are therefore perpendicular to the plane of the 
latter. Hence every secondary bisects its great cir- 
cle ; a secondary also bisects every small circle tliat 
is parallel to the great circle to wliich it is secondary. 
Since every secondary passes through the pole of its 
great circle, and is perpendicular to it ; it follows, 
that if a secondary passes through the poles of two 
great circles, it is perpendicular to each of them. 
And conversely, if one circle be perpendicular to two 
others, it must pass through their poles. 

55. The above definitions belong wholly to the Poles of the 
sphere considered abstractedly as a geometrical solid ; terrestrial 
the following appertain to the sphere considered with sphere. ' 
reference to astronomy. 

1. Let pep' of (fig. 19) represent the earth which Fig. 19. 
at present we shall consider as a perfect sphere, and 

let pp' be the line about which it performs its diurnal 
rotation ; then pp' are called its poles, and the line 
p p' its axis. And if we assume tlie circle PEP'Q to 
denote the circle of the celestial sphere, and conceive 
pp' to be produced to the heavens meeting them in 
PP^ these will be the poles of the celestial sphere. 

2. The terrestrial equator is a great circle erqs, of 
the earth perpendicular to its axis ; and if we con- 
ceive the plane of this circle to be produced to the 
sphere of the fixed stars, it will mark out the great 
circle ERQS, which is called the celestial equator. 

Hence it follows, that the poles of the terrestrial 
and celestial spheres are the same as the poles of the 
respective equators. 

The equator divides either spheres into two equal Equator, 
portions, called the northern and southern hemispheres, 
and the corresponding poles are in like manner deno- 
minated the north and south poles. The northern he- 
misphere is the part of the earth v/hich lies on tlie 
side of the equator v.hich we inhabit, and which in 
the figure we may assume to be ep q. 

2. Tlie latitude of a place on the earth's surface is Latitude- 
its angular distance from the equator, measured upon terrestrial. 
a secondary to it: tlius the arc eb, measures tlie 
latitude of the point b. Any circle on which we 
measure the latitude of a place is called a terrestrial 
meridian; and when produced to the heavens a celes- Meridian. 
tial meridian. 

3. Tlie small circles parallel to the terrestrial equa- 
tor are called parallels of latitude. 

4. The secondaries to the celestial equator are called 
circles of declination ; and the small circles parallel to 
the equator on the earth's surface parallels of declina- 
tion. Declination, therefore, in the celestial sphere, 
corresponds to latitude on the terrestrial sphere, thus 
the arc eb M-hich measures the latitude of a place on 
the earth, corresponds to EZ, the declination in the 
heavens. 

5. The longitude of a place on the earth's surface Longitude 
is an arc of the equator, mtercepted between the me- terrestrial 
ridian passing through the place, and another called a 

first meridian, passing through that place from which 
you begin to measure ; which latter is different in 
different countries. Most nations account their first 



522 



ASTRONOMY. 



Astronomy. 



Zenith i 
nadir. 



Vertical 
circles. 



Prime ver- 
tical. 



Azimuth 
and ampli 



Ecliptic. 



Obliquity 
of the 
ecliptic. 



meridian that passing over their capital. The English, 
for example, take the meridian of London, or rather 
that ofthe Royal Observatory, Greenwich J the French, 
that of Paris, &c. 

6. If b be supposed to denote any place on the 
earth, and a tangent plane be supposed to be drawn 
to that place, and produced to the heavens, meet- 
ing them in the points a c, the circle a b c, which 
is here projected into a right line, is called the sensible 
horizon. 

And the great circle HOR, which is drawn parallel 
to it, passing through the centre of the earth O, is 
called the rational horizon. It is in the former of those 
circles, which all the heavenly bodies are observed to 
rise and set. 

Small circles parallel to the horizon are called 
almucantars. 

7. If the radius O b of the eartli at the place 6 of a 
spectator be produced both ways to the heavens, that 
point Z vertical to him is called the zenith, and the 
opposite point N the nadir. Consequently, the zenith 
and nadir are the poles of the rational horizon. 

8. Vertical circles are those secondaries Avhich are 
perpendicular to the horizon, and which therefore 
pass through the zenith : it is in these circles the 
altitude of the heavenly bodies are taken. The celes- 
tial meridian of a place is therefore a vertical circle 
passing through the pole and zenith of that place ; as 
PEHP^ in the figure above referred to. 

The two points in the horizon R H, which are cut 
by the meridian of any place, are called the north and 
south points, according as they are towards the north 
or south poles. 

9. That vertical circle which cuts the meridian of 
any place at right angles, dividing it into two equal 
hemispheres, and which cuts the meridian in tlie east 
and west points, is called the prime vertical, as ZN, 
which is projected into the right line ZN. 

10. When a body is referred to the horizon by a 
vertical circle, the distance of that point of the hori- 
zon from the north or south points, is called the azi- 
muth, and its distance from the east or west points its 
amplitude. 

11. The ecliptic is that great circle of the heavens 
which the sun appears to describe in the course of the 
year. 

12. The angle which the ecliptic forms with the 
celestial equator, is called the obliquity of the ecliptic; 
and the two points in which these circles intersect and 
bisect each other, are called the equinoctial points. The 
limes when the sun comes to these points are called the 
equinoxes. 

For the signs, order, and characters of the twelve 
signs of the ecliptic, or zodiac^ see our table of con- 
stellations, p. 506. 

Of these signs, the first six which lie on the north- 
ern side of the equator, are called northern signs ; 
viz. Aries, Taurus, Gemini, Cancei, Leo, Virgo : and 
the other six. Libra, Scorpio, Sagittarius, Capricornus, 
Aquarius, Pisces, the southern signs. 

The equinoctial points correspond to the first points 
of Aries and Libra. 

The six signs, Capricorn, Aquarius, Pisces, Aries, 
Taurus, and Gemini, are called ascending signs, the 
sun approaching our's, or the north pole, while it 
passes through them ; the others. Cancer, Leo, &c.. 



are, for a corresponding reason, called descending 
signs ; the sun, while passing through them, being ; 
receding from our pole. 

14. The zodiac is a zone of the celestial sphere, 
extending 8° on each side of the ecliptic, within which 
the motion of all the principal planets are performed. 

The signs of the ecliptic and of the zodiac are the 
same. 

, 15. When any of the heavenly bodies appear to 
move according to the order of the signs, viz. through 
Aries, Taurus, &c. their motion is said to be direct, or 
in consequentia ; when contrary to that order, retro- 
grade, or in antecedeatia. (See art. 29) 

The real motion of all the planets is according to 
the order of the signs. 

16. We have seen, that the declination of any 
heavenly body is measured by the arc of a declination 
circle, or secondary to the equator, and the distance 
of that secondary on the equator from the first point 
of Aries, estimated according to the order of the 
signs, is called its right ascension. 

Hence the right ascension of a heavenly body cor- 
responds with the longitude of a terrestrial one, ex- 
cept as to the point whence it is measured. 

17. The latitude of a heavenly body is measured by 
a secondary to the ecliptic passing through that body ; 
that is, by the angular distance between it and the 
ecliptic, as by the arc m s, fig. 20 : and the longitude 
is measured by the arc of the ecliptic, intercepted be- 
tween the first point of Aries and the point where the 
secondary meets the ecliptic, estimated according 
to the order of the signs, as o m, considering o as the 
first point of Aries. 

Hence the latitude and longitude of a heavenly body 
are the same with reference to the ecliptic and its 
secondaries ; as those of a terrestrial body or place 
with reference to the equator and meridians. 

18. The oblique ascension is an arc of the equator, 
intercepted between the first point of Aries, and that 
point of the equator which rises with any body ; and 
the difference between the right and oblique ascension 
is called the ascensional difference. 

19. The tropics are two celestial circles parallel to 
the equator, and touching the ecliptic ; the one at the 
beginning of Cancer, called the tropic of Cancer ; the 
other at the beginning of Capricorn^ called the tropic 
of Capricorn. The two points where the tropics touch 
the ecliptic, are called the solstitial points. 

20. The arctic and antarctic circles are two parallels 
of declination ; the former about the north, and the 
latter about the south pole : the distance of each from 
the pole is equal to the distance of the tropics from 
the equator. 

These two circles, and those of the tropics, when 
referred to the earth, divides it into five zones ; two 
called the /rigid zones, whicli are those towards the two 
poles ; the temperate zones being those between each 
tropic and its corresponding polar circle ; and one 
torrid zone, including aU the space between the two 
tropics, extending therefore about 23 j-° on each side 
of the equator. 

21. The nodes are the points where the orbit of a 
planet cuts the plane of the ecliptic ; and the nodes of 
a satellite, are the points where its orbit cuts the plane 
of the orbit of its primary^ or that about which it re- 
volves. 



Direct and 
retrograde. 



Right as- 
cension. 



Latitude 
and longi- 
tude in the 
heavens. 
Fig. 20. 



Oblique 
ascension. 



Tropics. 



Arctic and 

antarctic 

circles. 



Nodes. 



ASTRONOMY. 



523 



Astronomy. The ascencU72g node is that where the body passes 
''^"-^^'■^ from the south to the north side of the ecliptic, and 
the other is called the descending node. 

22. Tlie aphelion is that point of the orbit of a planet 
which is farthest from the sun ; and the perihelion that 
point where it is nearest. 

The apogee and perigee have the same signification 
with reference to the earth. The moon, for instance, 
is said to be in apogee when farthest from us j and in 
perigee, when nearest. 

The above definitions will be sufficient for our pre- 
sent purpose ; others, which require a previous know- 
ledge of certain subjects not yet discussed, are reserved 
for those places in the course of the subsequent sec- 
tions in which they naturally occur, 

2. Illustration of certain celestial phenomena. 
General re- 5g_ Let US now proceed to show the application of 
marks on ^^^ doctrine of the sphere, to the illustration of cer- 
sphere. t^'" celestial phenomena, as the rising, setting, south- 
ing, &c. of the heavenly bodies. 

57. In art. 55. we have defined the sensible and 
rational horizon ; but with reference to the sphere of 
the fixed stars, these may be considered as coinciding, 
the angle which the arc H a (fig. 19) subtends at the 
earth, becoming then insensible in consequence of the 
immense distance of these bodies. Now, if Ave sup- 
pose, as we have hitherto done, the earth to revolve 
daily about its axis, all the heavenly bodies must suc- 
cessively appear to rise and set, or revolve about the 
pole, in circles, whose planes are perpendicular to the 
earth's axis, and consequently parallel to each other ; 
and Avill, to every appearance, be the same as if the 
spectator were at rest in the centre of a concave sphere, 
Avhich revolved uniformly about him ; or that the 
stars each revolved in parallel circles on such a sphere. 
We may therefore consider the earth but as a point 
with reference to the radius of the sphere of the fixed 
stars, and leave it out of the consideration in our far- 
ther inquiries upon tliis subject, and only employ the 
zenith, equator, poles, horizon, &c. of the celestial 
sphere, and such circles of declinations, as correspond- 
ing with the motion of the given bodies. 
Oblique 58. Let then fig. 21. represent the position of the 

sphere con- jjeavens to an observer, whose zenith is Z in north 
fS zT."'' latitude ; EQ the equator, PP' the poles, HOR the 
rational horizon, PZHP'R the meridian of the spec- 
tator. 

Draw the great circle ZON perpendicular to the 
meridian, and passing through the zenith Z, which 
from our definition will be the prime vertical ; and 
being in the plane of the eye, this being supposed to 
be perpendicular over the pole of the meridian, will 
be projected into a right line ZN, as will be shown in 
9ur treatise on Projection and Perspective. The same 
will also be the case with the equator EQ, the horizon 
HR, and the great circle POP', supposed to be drawn 
perpendicular to the meridian ; the common inter- 
section of all these circles being in the point O, the 
pole of the meridian. 

Draw the small circles, or parallels of declinations, 
tu H, m t, ne, R u, y x, which will represent the cir- 
cles described by any of the heavenly bodies j and as 
the great circle POP' bisects the equator, it will 
bisect all the small circles parallel to it, conse- 
quently mt, ae, are bisected in r and c ,• and we 



apparition. 



shall have ac=. ce, and mt=rt, each equal to a P'ane 
quadrant, or 90°. Astronomy. 

Now if we conceive the figure referred to as exhi- """"^v^"^ 
biting the eastern hemisphere, the several arcs QE, 
a e, t m, &c. will represent the paths of bodies placed 
at those distances from the pole, as they ascend from 
the meridian under the horizon to the meridian above ; 
and the points h, O, s, will be the places where they 
rise, or begin to appear above the horizon ; and i E e, 
the points where they attain their greatest or meridian 
altitude ; as a e, QE, m t, are bisected in c, O, r ,• e b 
must be greater than h a; QO, equal to OE, and ts 
less than * m. 

Whence it follows, that a body on the same side of 
the equator as the spectator, will be longer above the 
horizon than below it ; when the body is in the equa- 
tor it will be as long below as above the horizon ; and 
when it is on the contrary side of the equator to the 
spectator, it will be longer below the equator than 
above it ; for the arc e 6 is greater than b a, EO=OQ, 
and t s less than s m, and the motion with which these 
arcs are described are uniform. 

The bodies describing a e, m t, rise at h and 5 ; and 
as O is the east point of the horizon, and H and R the 
north and south points ; a body on the same side of 
the equator as the spectator rises between the east 
and the north ; and a body on the contrary side, be- 
tween the east and the south, the spectator being 
supposed in north latitude ; and a body in the equator 
rises in the east at O. 

59. When bodies come to d and r, they are in the Circles of 
prime vertical, or in the east ; hence, a body on the ^"^^|^;^, 
same side of tlie equator as the spectator comes to the 
east after it has risen ; a body in the equator rises in 
the east, and one on the contrary side of the equator 
has passed the east before it rises. The body which 
describes the circle Ri;, or any one nearer to P, never 
sets ; and such circles are called circles of perpetual 
apparition, and the stars which describe them circum- 
polar stars. The bodyAvhich describes the circle wH, 
just become visible at PI, and then instantly descends 
below the horizon ; but those bodies which describe 
the circles nearer to P' are never A'isible. 

Such is the apparent diurnal motion of the heavenly 
bodies, when the spectator is situated any where be- 
tween the equator and either poles ; and this is called 
an oblique sjjhere ; because all bodies rise and set 
obliquely to the horizon. 

In the above deductions we have supposed the figure 
to represent the eastern hemisphere, and the bodies 
to ascend through their respective arcs ; but it may 
be equally supposed to denote the western hemi- 
sphere, only in this case, these arcs will represent the 
paths of the body as they descend from their greatest 
altitude above the horizon to their meridian beloAv the 
horizon. And hence, it is obvious, that supposing a 
body not to change its declination, it will be at equal 
altitudes at equal times before and after it has attained 
its meridian altitude. 

60. In the preceding article we have supposed the Right 
spectator to be in north latitude, or, which is the ^Pl^^re 
same, the zenith of the spectator to be between the 
equator and north pole ; and it is obvious, that what 
we have said would apply equally to a spectator simi- 
larly situated in south latitude; but when he is 
situated either in the equator or in one of the poles. 



524 



ASTRONOMY 



Astronomy. 



Fig. 22. 



Parallel 
sphere. 
Fig. 23. 



Of the 
change of 



Apparent 
motion of 
the sun. 



Change of 
seasons. 



the considerations become less complicated ; in the 
former case we call it a right sphere, and in the latter a 
parallel sphere. If the spectator be at the equator, 
then E coincides with Z, and Q with N, as in (fig. 
9.2) ; consequently also PP' coincides with HR ; and 
the declination circles ea, tm, which are always paral- 
lel to the equator, are in this case perpendicular to the 
horizon ; and as these circles are always bisected by 
PP', they must now be bisected by the horizon HR ; 
hence in tliis position of the spectator all the heavenly 
bodies, which change not their declination, will be 
an equal time above and below the horizon, and will 
rise perpendicularly to it ; whence the denomination 
of the right sphere. 

On the other hand, if the spectator be situated 
at the pole, then the sphere will be as represented in 
fig. 23, that is, we shall have P coincide with Z, and 
EQ, with HR, or the equator will coincide with the 
horizon ; and all the parallels of declination, ae, mt, 
described by the heavenly bodies, Avill be therefore 
parallel to the horizon ; any body, therefore, which is 
above the horizon, and which changes not its declina- 
tion, will remain constantly above the horizon, and 
at the same altitude ; and those which are below the 
horizon will continue constantly below. Conse- 
quently, a spectator at the pole would never see the 
heavenly bodies rise and set, but would observe them to 
describe circles in the heavens parallel to the horizon ; 
whence the denomination parallel sphere. 

61. We have had two or three times occasion to 
use the words, " those heavenly bodies which change 
not their declination ;" it may be here proper to ex- 
plain to the reader, that by this we mean the fixed 
stars only, these being the only celestial body that 
are not subject to a change of declination ; and some 
of these even are liable to such a change, it is however 
too inconsiderable to be attended to in this place. But 
the sun, moon, and planets are constantly changing 
their declination, in consequence of the proper motion 
of the earth and themselves ; let us, therefore, now 
bestow a few words in explanation of these cases, par- 
ticularly as regards the sun. 

We have already stated in our introduction (art.27) 
that by attentively observing the stars which set and 
rise with the sun during the course of the year, that 
he appears to have described a great circle of the 
celestial spliere, forming with the ecliptic an angle of 
about 23i°, or more exactly 23° 28'. This circle is 
called the ecliptic, and is denoted by the line LC, into 
which it is projected in the three last figures ; which 
circle cuts the equator, as we have seen, in two points 
called the equinoctional points. Tlie sun, therefore, 
during one part of the year, is on one side of the equa- 
tor, and in the other, on the contrary side ; and by 
this means his rising and setting is subject to all that 
variety which we have noticed in the stars in the two 
hemispheres, and hence the cause of the different 
lengths of the days at different times of the year, the 
succession of seasons, and the several phenomena at- 
tending them, as we have already endeavoured to 
explain in a popular manner in the preceding intro- 
duction. 

Let us now endeavour to illustrate the same a little 
more particularly by referring again to our fig. 2J. 
Here since in the course of the year, the sun appears 
to de cribe the circle of which LC is the projection, it 



is obvious that he will be sometimes to the north of Plane 
the equator, as in q, at others to the south, as in p, Astronomy, 
and at others in the equator, as at O. In the former ^— V"^ 
case, that is, when he is in q, P denoting the north 
pole, it is obvious, as we have already remarked re- 
specting any body describing the declination circle ae, 
that he will rise between the north and east, attain to 
the prime vertical, after he has risen, and will be 
longer above the horizon than below it, which is the 
case in our latitudes, from about the 2Ist of March to 
the 22d of September, these being nearly the times 
when the sun crosses the equator. On those two days 
he rises in the east, and is an equal time above and 
below the horizon to every part of the globe except 
the two poles ; and the days and nights being then 
equal, these points are called the equinoctial points, 
and the sun itself is said to be in the equinoxes. The 
former of these is called the vernal^ and the latter the 
autumnal equinox. When the sun is on the south 
side of the equator, as at p, then the same j-emarks 
apply as we have already made with respect to any 
body describing the declination circle, m t, that is, he 
will rise between the south and the east, and will be 
longer below than above the horizon, and our days 
will be shorter than our nights, as is the case from the 
autumnal to the vernal equinox, that is, from about 
the 22d of September to the 21st of March. 

When the spectator is in the equator, then the 
sphere being right (see fig. 23), the sun will be 
always an equal time above and below the horizon j 
and when the sun is also in the equator, he will rise 
east and describe a great circle corresponding with the 
prime vertical, and will be vertical over the head of 
the spectator in the middle of his course : at other 
times he will rise between the north and the east or 
the south and the east, according as his declination is 
north or south. There is, therefore, even in these re- 
gions, a change of seasons ; but as the sun will dart 
his vertical beams upon every point of the equator, twice 
in the course of one revolution, the inhabitants may 
be said to have two summers and two winters in the 
course of a year. When the spectator is at the pole, 
the sphere will be parallel (see fig. 23), and the sun 
from the vernal to the autumnal equinox, will be con- 
stantly visible to the north pole, and perpetually hid- 
den below the horizon during the other half of the 
year ; and the contrary for the south pole. That is, 
in the former, he will be visible from the time he 
passes from O to L, and from L to O, and be invisible 
while he is describing the other half of the ecliptic. At 
each of the poles, therefore, the days and nights are 
each half a year in length. It must not, however, be 
understood here, that the length of the days and 
nights are each exactly equal to half a year, for we 
shall see hereafter, tliat the sun is not so long on the 
northern as on the southern side of the equator, the 
cause of which will likewise be illustrated in a subse- 
quent chapter. At present, it will be sufficient to ob- 
serve, that such is known to be the case from obser- 
vation. 

62. We have seen in our definitions that the earth Zones de- 
ls considered as divided into five zones, by referring scribed. 
to the earth the two polar circles, and the two tropics. 
Now from what has been above stated, it is obvious, 
that to an observer in either hemisphere, in the lati- 
tude of 23° 28', his zenith wiU coincide with the sun's 



ASTRONOMY. 



525 



Astronomy, place at noon, on that day when it has attained its 

■ sT'^ greatest north declination, if the observer be in north 

latitude ; or south, if he be situated in south latitude ; 
consequently, in either situation, on one day in a year 
the sun will be vertical to the inhabitants of either 
tropic, and of course to all places situated between 
them, except those on the equator, who, as we have 
seen, have the sun vertical twice. 

Beyond the tropics, either to north or south, the 
sun is never vertical, the zenith of all such places 
being farther from the equator than the extreme de- 
clination of the sun or the obliquity of the ecliptic. 

Those who inhabit the two polar circles will have 
one day and one night of twenty-four hours, or there 
will be one day in each of those circles when the sun 
will not set, another on which he will not rise, as will 
be immediately obvious by referring to the preceding 
figures. 

From these circles to the poles themselves the sun 
will be for a greater or less time above and below 
the horizon, till in the actual poles, the nights and 



days will be half a year each, as we have already piane 
stated. Astronomy. 

3. SijnoTpus of spherical trigonometry. S^^^^^Z^i 

62. As in the course of the following articles, we spherical 
shall have frequent occasion to refer to the several trigonome- 
cases of spherical trigonometry, we conceive that it '''^' 
will be very convenient for the reader to have a gene- 
ral synoptic table of all tlie principal results and 
theorems belonging to this doctrine, the investigations 
of which will be given in our Treatise on Trigonome- 
try, Part I. We collect them here merely for the 
convenience of reference, and have chosen those only 
which are most general in their application. They 
are sufficient for the solution of any spherical pro- 
blem, although, in certain cases, they may not offer 
the most expeditious mode of solution ; we shall not 
therefore uniformly adopt the formulae given in the 
table, but when a more expeditious form presents it- 
self, we shall avail ourseh'es of it ; in the greater 
number of cases, however, our solutions will be de- 
duced from the tabula formulce. 



Table .1. For the solution of all the cases of right angled spherical triangles. 



Hypothenuse 
and one leg. 



One leg and its 
opposite angle. 



III. 

One leg, and the 
adjacent angle. 



IV. 

Hypothenuse 
and one angle. 



Required. 



Angle opposite 
the given leg. 
Angle adjacent to 
the given leg. 

Other leg. 



Hypothenuse. 
Other leg. 
Other angle. 



Value of the Terms required. 



Its sin 



Its cos 



Its cos 



sin given leg 
sin hypoth. 

tan given le^ 
tan hypoth 
cos hypoth. 

cos given leg 



Its sin 



Its sin 



Its sin 



sin given leg 
sin given ang. 
tan given leg 
tan given ang. 
cos given ang. 
cos given leg 



Cases in which the terms requir- 
ed are less than 90". 



If the given leg be less than 
90°. 

If the things given be of 
the same affection*. 

Idem. 



Ambiguous. 

Idem. 

Idem. 



Hypothenuse. 

Other angle. 
Other leg. 



Adjacent leg. 

Leg opposite to 
the given angle. 

Other angle. 



The two legs. 



VI. 

The two angles 



Hypothenuse. 

Either of the an- 
gles. 



Hypothenuse. 
Either of thelegs 



I Its tan = '^^L4^J^ I 

L cos given ang. J 

Its cos = cos giv. leg x sin giv. ang. | 
Its tan = sin giv. leg tan giv. ang. | 



Its tan = tan hyp. x cos giv. ang. < 

> Its sin = sin hyp. x sin giv. ang. 

/ Itstan = ^^"-""g^^ ) 

L cos hypothen J 



Its cos 



rectan. cos given legs 

_ tan opposite leg 
sin adjacent leg 



If the things given be of 
like affection. 

If the given leg be less 

than 90°. 
If the given angle be less 

than 90°. 



If the things given be of 
like affection. 

If the given angle be acute. 

If the things given be of 
like affection. 



If the given legs be of 
like affection. 

If the opposite leg be less 
than 90°. 



Its cos = rect. cot given angles 
cos opposite .ingles 



Its cos = 



sin adjacent angle 



} 



If the angles be of like af- 
fection. 



If the opposite be ac 



;ute. 



* Angles or sides are of the same affection when they are both greater or both less than a right angle ; and in tlie tliird column 
of our Table we have stated when the result is of the same affection with the things given, and when it is ambiguous. 
VOL. in. 3 Y 



52G 



ASTRONOMY. 



Astronomy, In working by logarithms the reader must observe, 

^— ~Y— »^ that when the resulting logarithm is the log. of a 

quotient, 10 must be added to the index ; and when it 

is the log. of a product, 10 must be subtracted from 

the index. Thus, when the two angles are given, 

log. cos hypothenuse = log. cos one angle + log. 
cos other angle — 10. 

log. cos either leg = log. cos opp. angle — log. sin 
adjac. angle + 10- 

Quadrantal triangles. 

In a quadrantal triangle if the quadrantal side be 
called radius, the supplement to the angle opposite to 
that side be called hypothenuse, the other sides be 
called angles, and their opposite angles be called legs ; 
then the solution of all the cases will be as in the 
above table for right angled spherical triangles. 



Napier's analogies for right angled spherical tri- Plane 

angles. Astronomy. 

Napier's circular parts are, the complements of the ^""V"""^ 
two angles that are not right angles, the complement 
of the hypothenuse and the other two sides ; that is, 
denoting the sides by a, b, c, and the angles by A, B, C, 
A being the right angle, the parts are 90^— a, 90°— B, 
90°— C, and b, c; of these, anyone may be the middle 
part, and the two parts next adjacent, one to either 
hand (not including the right angle) the adjacent 
parts ; and the otlier two the opposite parts ; then 
the analogies are 

rad X sin middle part = rectangle of the tangents 
of adjacent parts. 

rad X sin middle part = rectangle of the cosines of 
the opposite parts. 

And by making the transformations above explained, 
these will also apply to quadrantal spherical triangles. 



Table II. For the solution of oblique angled spherical triangles. 



Required. 



Values of the quantities required. 



I. 

Two angles and 
a side opposite to 
one of them. 



Side opposite to 
other angle. 



Third side. 



Third angle. 



r By common ana- ~) 
1 logy / 

/ Let fall a perpen- "^ 
\ dicular upon the ff 
<^ side contained V 
i between tlie giv- 1 
(^en angles. J 

r Let fall a per. as 
l_ before 



Sines of angles, are as sines of opp. sides. 

Tan 1 seg. of this side = cos adj. angle X tan 
given side. 

sin 1 seg. x tan ang. adj. given side 
Sin 2 seg. ;= 



tan ang. opp. given side. 

Cot 1 seg. of this ang. = cos giv. side x tan adj. 
ang. 

sin 1 seg. x cos ang. opp. given side 
Sin 2. seg. x ^ ^ '' ^ 



cos ang. adj. given side. 



II. 

Two sides and an 
angle opposite to 
one of them 



The angle oppo- 
site to the otlaer 
side. 



Angle included 
between the giv- 
en sides. 



Third side. 



_By tire common"! 
"analogy. J 



"^ Letfallaperpen- 
> dicular from the< 
J included angle. 



/ Let fall a perpen- \ 
\ dicular as before. / 



Sines of sides are as sines of their opposite angles 

Cot 1 seg. ang. req. = tan giv. ang. x cos adj 
side. 

cos 1 seg. X tan giv. side adj. giv. ang. 

Cos 2 seg. = 7 -. ^ 

tan side opp. given angle. 
Tan 1 seg. side req. = cos giv. ang. x tan adj 
side. 

cos 1 seg. X cos side opp. giv. ang 



cos side adj. given angle. 



III. 

Two sides and the 
ncluded angle. 



An angle oppo- 
site to one of the 
given sides. 



Third side. 



"^ Let fall a perpen - 
> dicular from the< 
J third angle. 



rLet fall a perpen-' 
< dicular on one ( 
Lthe given sides 



Tan 1 seg. of div. side = cos giv. ang. x tan side 

opp. ang. sought. 
^ ^ tan giv. ang. x sin 1 seg. 

Tan ang. sought = ^ 2_^ _^- 

sin 2 seg. or div. side. 
Tan 1 seg. of div. side = cos giv. ang. x tan other 

given side. 






Cos side sought : 



cos side not div. x cos 2 seg. 



cos 1 seg. of side divided. 



Cot 1 seg. of div. ang. = cos giv. side x tan ang. 

opp. side sought. 
„ . , , tan s\v. side X cos 1 seg. div. ang. 

Tan side sought = ^- . .. . . ° r-^ 

cos 2 seg. or divided angle. 

Cot 1 seg. div. ang. = cos given side x tan other 

giv. angle. 
^ , , cos ang. not div. X sin 2 seg. 

Cos angle sought = ^^ ;; 

sin 1 seg. div. angle. 



IV. 

A side and the 
two adjacent an- 
gles. 



A side opposite 
to one of the 
given angles. 



Third angle. 



Let fall aperpen- 
• dicular on the 
third side. 



/^Let fall a perpen- 
J dicular fror 
J of the gi 
Vgles. 



1 perpen- r 
From one J 
;iven an- j 



ASTRONOMY. 

Table II. — Continued. 



527 



Astronomy. 



V. 

The three sides. 



VI 



The three angles 



Reqiurcil. 



An angle by the 
sine or cosine of 
its half. 



Aside by the sine 
or cosine of its 
half. 



Value of the quantities required. 



I 



Let a, b, c, be the three sides ; A, B, C, the angles ; h and c, includ- 
ing the angles sought, and s = a + 6 + c. Then^ 
'sin. (5S — h) sin (|s — c) 



sin ^ A 



V SI 



sin b sin c. 
sin (^ s — «) 



sin b. sin c. 



Let S be the sum of the angles A^, B^ C;, and B and C be adjacent to 
a, the side required ; then, 
... / cos I S cos (I S — A) 

smi A=\/ 

V s 



!— 2 y si 

cosIA=y-^^ 



sin B. sin C. 

S - B) sin (§ S - A) 



sin B. sin C. 



Plane 
Astronomy. 



Table III. 
For the solution of all the cases of oblique angled spherical triangles, hj the analogies of Napier. 



Given. Required. 



Value of the terms required. 



I. 

Two angles and 
the sides opposite 
to one of them. 



Side opposite to 
tlie other given 
angle 

Third side. 

Third angle. 



By the common analogy ; viz. 

The sines of the angles are as the sines of the opposite sides 

tan i dif. giv. sides x sin § sum opp. ang. 
sin i dif. of those angles, 
sum giv. sides X cos \ sum opp. ang 
cos 5 dif. those angles. 
By the common analogy. 



tan of its half 



^ _ tan A I 
Y^t_an£ 



Two sides and an 
opposite angle. 



Angle opposite to 
the other known 
side. 



Third angle. 
Third side. 



-By the common analogy. 



cot of its half 



^If j _ tan| 



tan § dif. other two ang. x sin \ sum giv. sides 
sin 5 dif. those sides, 
svim other two ang. x cos § sum giv. sides 
cos h dif. those sides. 



By common analogy. 



Ill, 

Two sides and 
the included an- 
gle. 



The two other 
angles. 



Third side. 



I vp '^'^^ 2 S^^'" '^'^S'^^ ^ ^^'^ 2 ^^^- given sides 
^ ' sin I sum of those sides. 

cot I giv. angle x cos 5 dif. given sides 
cos 5 sum of those sides. 
By the common analogy. 



tan i sum. 



IV. 

Two angles and 
the included side. 



The other two 
sides. 



Third angle. 



T ,.„ tan i giv. side x sin i dif. giv. angle 

tan i dif. = ^-2 — ± 2 2 — 

sin i sum of those angles 
tan i giv. side x cos \ dif. giv. angle 
cos I sum of those angles. 
By common analogy. 



tan ^ sum 



The three sides. 



Either of the an- 
gles. 



Let fall a perpendicular on the side adjacent to the angle sought ; 

then, 
' tan i sum or | dif. of the seg- "1 _ tan \ sxvca x tan § dif. of the sides 

ments of the base / tan - base. 

Cos angle sought = tan adj. seg. x cot adj. sides. 



Yl. 

Tlie three angles. 



Either of the 
sides. 



rThese will be determined, by finding the corresponding angle, by the 

i^ last case, of a triangle, which has all its parts supplemental to 

L those of the triangles, whose three sides are given. 

_— — 



528 



ASTRONOMY. 




To deter- 
mine tlie 
latitude of 
the place. 



By obser- 
vations on 
the circum- 
polar stars 



Astronomy. 4. Problems relative to the determination of t/ie posi- 
tion of the lieavenly bodies. 

63. It is obvious from wliat we have stated relative to 
the position of the different circles of the sphere, that 
one of the most inciportant data in the solution of as- 
tronomical problems is the latitude of the place of the 
observer^ from which the zenith Z in the preceding 
figures is determined. ' This may be found as follow. 

Problem I. 

To find the latitude of anij place on the earth's surface. 

1 . Observe the altitude of the pole above the hori- 
zon of any place, and that altitude will be equal to the 
latitude. 

The latitude of any place on the earth is measured 
by the arc EZ, that is, by the arc subtended between 
the equator and zenith. But EZ -f ZP = 90'^ and 
ZP -1- PR = 90^ ; whence 

EZ + ZP = ZP -f PR 
Consequently EZ = PR 
That is, the latitude of any place is equal to the ele- 
vation of the pole above the horizon of that place. 

The elevation of the pole above the horizon, may 
be practically determined by observing the greatest 
and least altitude of any of the circumpolar stars, and 
taking half the sura of the two altitudes ; the proper 
corrections being made for refraction, parallax, &c. 
according to the principles explained in a subsequent 
chapter. 

For let xy, fig. 21, represent the circle of declina- 
tion described by any circumpolar star, then R.r will 
be its greatest meridian altitude, and Rj/ its least, and 
it is obvious that 

RP = § (Ry -FR^) 

2. The latitude may also be found by observing the 
altitudes of the sun when he has attained his greatest 
north and greatest south declination. Half the sum 
will be the elevation of the equator above the horizon, 
and the complement of that angle the latitude of the 
place of the observer. 

Referring to the same figure, let ea be the declina- 
tion circle described by the sun when he has the 
greatest north declination, then eH will be his great- 
est altitude on that day ; let s i in like manner be the 
declination circle described on the day when he has 
the greatest south declination ; then H e, will be its 
meridian altitude on that day ; and since E e ;= Es, it 
is obvious that 

HE = l(He + Hs) 
And 90° — HE = EZ the latitude. 

64. It is obvious, also, from what is stated above, 
and referring to our definition of the obliquity of the 
ecliptic, that this angle is measured by half the arc 
se, that 

§ (He — Hs) = the obliquity of the ecliptic 

Problem II. 

To find the time of the rising, setting, &;c. of the heavenly 
bodies. 

To find the 65. Let the proposed body be the sun, and let us 
timeofris- suppose that its declination remains constant during 
ing, &c jjg passage from one meridian to the other, and that a 
clock is adjusted to go 24 hours during this one appa- 
rent revolution of the sun, and moreover^ that the 



By obser- 
vations on 
the sun. 



clock shows 12 exactly, when the sun is on the meri- Plane 
dian ; to find the time of its rising, and its azimuth at Astronomy. 
that time ; the latitude of the place and the declination ^ — y — '' 
of the sun being given. 

Referring to lig. 24, and comparing it with what Fig. 24. 
has been stated with reference to fig. 21 (art. 59,) it 
appears that the sun rises when it comes to b ; that 
it is twelve o'clock when the sun is upon the meridian 
at e, and that the whole circle a e a is described in 24 
hours ; that is uniformly at the rate of W° = 15° per 
hour ; to find the time of rising, therefore, we have 
only to compute the angle ZP6, and to convert it into 
time at the rate of 15° to an hour in time ; and to find 
its azimuth from the north we must compute the an- 
gle RP6, for which computations we have the fol- 
lowing data : 

bZ = 90°, Ee = declination ; eP = P6 co-declination 
EZ = latitude ; ZP = co-latitude 
Hence in the triangle ZP6, we have the three sides 
given and one of them Zb = 90°, to find the angle 
ZP6. This case may therefore be solved by our fifth 
form in the preceding Table II. for oblique angled 
triangles, but one of the sides being 90°, it will be 
more readily solved by means of Napier's analogy j 
viz 

rad : cot 6P : : cot ZP : cos Z?b = hour angle 
or rad : tan.dec \ \ tan.lat \ cos ZP6 = hour angle 

Exam. 1. Let us, for example, suppose the latitude 
of the place to be 52° 13' north ; the declination 23° 
28', to find the time of sun's rising. 
By the above analogy, 

rad 100000000 

tan 23° 28'. . 9-6376106 

tan 52° 13'.. 101105786 

Cos 124° 2' 97481892 

(taking the supplement of the tabular angle 55° 58',. 
the angle being obviously greater than 90°.) 

According to either solution, therefore, we have the 
hour angle = 124° 2', 
which converted into time gives 

15° : 124° 2' : : Ih, : Sh. : 19i' time from noon 
consequently, 

h. m. //. 
12 O O 
8 19i 

3 40§ the time of rising 

That is in the latitude 52° 13', on the longest day, or 
when the sun has 23° 28' north declination, he Avill 
rise at 3h. 40§m. 

To find the azimuth from the north, we have in the 
same triangle the same data to find the angle PZ6, 
A/hich is the measure of the azimuth sought. This 
may therefore be determined by means of our form 5, 
oblique spherical triangles ; but more concisely by 
the following analogy : — 

sin ZP ; rad. ; \ cos 6P '. sin PZ6 := azimuth. 

Hence ar. com. cos 52° 13' 2127683 

rad 100000000 

sin 23 28 9-6001181 

cos 49° 32' azim 9-8128864 



ASTRONOMY. 



529 



Astronomy. ExAM. 2. Let it be required to determine the time 
^— -^N^^— ^ of sun rising- at the same place^ lat. 52° 13' on the 
25th of February, 1818. 

The declination on this day by nautical almanack 
is 9° II5' south. Consequently, referring to the same 
fig-. 24, 6' = 99" Hi'. Hence, then, in the trian- 
gle ZP6', we have as before, ZP = co. lat. = 37° 
47', PZ>' codec. 99° 11|', Z 6' = 90° Wlience. as in 
the former case, 

rad 10-0000000 

tan dec. 9° Hi' 92090197 

tan 52° 13' 101105786 

cos 77° 57' hour angle. . 93195983 

This converted into time gives 5h. 12m. from noon ; 
■which, taken from 12 hours, gives 6h. 48m. for the 
time sought. 

Problem III. 

Tofnd the suns altitude at 6 o'clock, azimuth, 8^c. 

Altitude at 66. Here, since PP' (fig. 25) bisects e a, it is clear 
60 ck)ck. ^jjg^j ^^g g^^j^ ^^.^Y\ be at c, at 6 o'clock ; and we have 
'^' "^' therefore, in this case, the hour angle ZP c = 90° 
given, and the two sides ZP, Pc, to find Zc, the co- 
altitude ; that is, two sides and the contained angle 
are given to find the third side. Whence, by our 
fifth form for right-angled sj)herical triangles, we 
have 

„ cos ZP X cos Pc 

cos Zc = 

rad. 

Or, which is the same, (adopting the data of the first 

of the preceding examples,) 

rad 10-0000000 

sin lat. 52° 13' 98978103 

sin dec. 23° 28' 9-6001181 

sin. alt. 18° 21' 9-4979284 

Time ol 67- To find at what time in the day the sun will be 

easting. east and west ; that is, in the prime vertical, and its 
altitude at that time ; taking the latitude of the place 
52= 12' 35", and the sun's declination 23° 28'. 

Here, taking ZP to denote the co-latitude = 37° 
47' 25" P b the co-declination ; and the angle b ZP 
being 90°, we have the two sides ZP, P b, of the 
right-angled spherical triangle b ZP, and the angle 
b ZP, a right angle, to find the hour angle ZP b. and 
the CO -altitude Z b. 

By preceding Table 1, form 1, 

„ , cos P b sin dec. 

cos Zi b = 7^^= -. — ; = sm alt. 

cos ZP sm lat. 

„„, tan ZP cos lat. 

cos ZP b = -— - = ■ — = hour angle. 

tanPo cos dec. 

sin dec. 23° 28' = 96001 181 

sin lat. 52° 12' 35" = 98977695 

sin alt. = 30° 15' 31" 9-7023486 

Again, cos lat. 52° 12' 35" = 9.8995301 

cos dec. 23 28 = 103623894 

cos hour angle = 70° 19' 44'-' 9-5371407 



Which, converted into time, gives 4h. 41' 19" from Plaoe. 
apparent noon. Astronomy. 

68. Given the latitude of the place, the sun's decli- "-^/-^ 
nation ; and altitude to find the hour and azimuth. ^Kn.om- 

Here, referring to the saine figure, we liave the 
co-latitude ZP, the co-altitude Z b, and the co-decli- 
natiqn P b to find the hour angle ZP b, and tiie azi- 
muth PZ b. That is, in a splierical triangle, we have 
three sides to find the angles. 

Whence, calling the sum of the three sides s, we 
have, by form 5, of our Table II., 

sin i s sin (^ s — Z b) ^ 
sin ZP . sin P b J 
Let the latitude be 34° 55', the declination 22° 22' 
57'' N, the altitude 36° 59' 39". Then ZP = 55° 5', 
Zb =53° 0' 21", P 6 = 67° 37' 3". Hence the 
operation, 

P6 = 67°37' 3" sin arith.comp. 00340191 
ZP=55 5 sinarith.comp. 00861939 
Z6= 53 21 



i cos ZP b 



= /{- 



sum 175 


42 24 


sin = 
sin = 




Is 87 
Z b 53 


51 12 
21 


9-9996942 
9-7569320 


-Z6=34 


50 51 


2)19-8768392 



cos PZ b 



/ f sin i s 



I cos ZP 6 = 29" 47' 44" = 9-9384196 
Hence, ZP 6 = 59° 35' 28", which, reduced to 
time, gives 3h. 58' 22" the-time from apparent noon. 
In the same manner 

sin {Is-Vb) -I 
sin Z Z) . sin ZP J 
The numerical solution of which, we leave as an exer- 
cise for the reader. 

69. By means of the azimuth determined as above. Meridian 
it will not be difiicult to draw a meridian line, by line, 
simply determining its position, so as to make tlie re- 
quisite angle with the direction of the sun at that 

time. This, however, of course supposes tliat the 
altitude of the sun has been properly corrected for re- 
fraction and parallax, which being subjects we have 
not yet touched upon, we merely indicate tlie principle 
of the determination, and shall leave our further dis- 
cussion on it to a subsequent chapter. 

70. In the preceding examples relative to those Error in al- 
questions in which the altitude is supposed to be de- titude. 
termined from observation, it is obvious that we not 

only suppose the requisite corrections to have been 
applied, but also that the observation is made without 
any appreciable error ; but as suclt error is easily 
made, particularly if the instrument be not of the 
most perfect construction, it may not be amiss to 
ascertain Avhat effect any such error will produce in 
the computed time, and the azimutli the sun ought to 
have, so that an error in altitude shall produce the 
least error in time ; we propose therefore the follow- 
ing problem. 

Pkoblebi IV. 
Given the error in altitude to find the error in time. 

71. LetEQ, fig. 26, represent the equator,? the pole, J^'e"'" 
a e the parallel of declination, in which the sun, or Fig. 26, 



I: 

i 



530 



ASTRONOMY. 



Astronomy, any other heavenly body is on the day of observation ; 
^^-— ^^^-».^ and let r be real, and s the apparent place of the 
body, or r « the error in altitude. Draw m s parallel 
to the horizon ; from Z, the zenith, draw Z m, Z r ; 
and from P the pole, the meridians P m p, Vrq, to 
pass through m r, and to cut the equator in the points 
p q, then m and r will be the real and apparent places 
of the body, on the parallel of declination ; and the 
arc m r on that circle, or the arc p q on the equator^ 
will measure the angle m P r, the corresponding error 
in time. Now the triangle m s r being of course ex- 
ceedingly small, it may be regarded as a rectilinear 
right-angled triangle, right angled at s ; 
and hence we have 

s r : r m '.', sin 5 m r : rad. 
by spherics mr : p q '.', cos q r : rad. 
Multiplying these together, rejecting the like factors, 
we have 

s r : pq '.'. sin s m r cos q r : rad .^ 
Whence 

rad.2 

p a = s r X -: 

sm sm r • cos q r 

But Z r P = s m r, s r m being the complement of each, 
and sin Z 7-P= (sin s m r) : sin PZ '. ', sin r ZP : sin Pr 
Consequently, 

sin s m r . sin P r = sin smr . cos qr = sin PZ . sin rZP 
Whence, substituting for the denominator in the above 
expression, its equivalent in the last, we have^ 
rad.® r s 

sin PZ • sin r ZP cos lat. sin r ZP 
taking radius == 1. 

Hence, since all tlie quantities in tliis expression 
are supposed to be given, except sin r ZP, it is obvi- 
ous, that p q will ceteris paribus be the least, when 
sin r ZP is the greatest, or when the azimuth is the 
greatest ; that is, when the body, whose altitude is 
observed, is in the prime vertical : it is best, there- 
fore, to deduce the time from an observation, when 
the body is in or near that circle. 

As an example in numbers, suppose the latitude to 
be 52° 12' 35'^ ; the declination 15^ 24' 25" ; and the 
altitude as corrected, 40" ; required the error in timd, 
supposing an error of 1" in the altitude. 
This gives 

1 



cos lat. sin azim, 
which answers to 7-528 seconds in time. 

Again, supposing the azimuth to be 46° 22', the 
latitude 52° 12'^ and the error in altitude V^ we have 

= 2'.334 of a degree = 9'''.336 in 



.612 X .690 



time. 



Time of the 72. By means of this solution, we may ascertain 
sun ascend- the time in which the sun will pass either the horizon- 
ing througli ^^y qj. vertical wire of a telescope : we have seen, for 
to i^trdia- instance, that the time during which the sun will 
meter, ascend through any small altitude = ?• s, or the arc 

that he will describe when referred to the equator 

during that time, is 



in which, substituting d'^ the apparent diameter of the Plane 
sun in seconds for r s, this becomes Astronomy. 



cos lat. sin . azimuth 



consequently. 



time in seconds. 



15 . cos lat. sin . azim. 
73. To find the time in which the sun will pass Time of its 
over the vertical wire, we may take m r to denote the Passing a 
apparent diameter of the sun ; then, as the seconds in ''^^^'^^■ 
m r, considered as a small circle, must be increased 
in proportion as the radius is diminished ; (because, 
when the arc is given, the angle is inversely as the 
radius,) we have 

sin Pr, or cos . dec. : rad : : (/" the seconds in mr. 
considered as a great circle, to the seconds in the 
same considered as a small circle, which are the 
seconds in p ^ ; whence 

rad. d" 

pq = ; = a . sec. dec. 

cos dec. 
and, consequently, 

d'' X sec. dec. 
the time = 



pq: 



cos lat. sin r ZP 



1.5'' 

Hence p q = d" sec. dec. expresses the sun's diameter 
in right ascension. If therefore we assume his appa- 
rent diameter at 32' = 1920", and its declination 20% 
its right ascension is 

1920" X sec. 20° = 34' 2" , 88 
which, divided by 15, will give the same in time. 

In the Nautical Almanack a column is given for in- 
dicating the time in which the semi-diameter of the 
sun passes over a vertical wire, by means of which a 
single observation on either limb;, may be referred to 
the centre. 

Problem V. 

To find the time when the apparent diurnal motion of a 
fijsed star is perpendicular to the horizon. 

74. Let^ 2/ (fig. 26) be the parallel of declination de- • 
scribed by the star ; draw the vertical Z h, touching it 

at ; then, when the star arrives at o, its apparent 
motion will be perpendicular to the horizon ; the two 
circles having in the point o, a common tangent. And 
Z P is a right angle, we have 

rad : tan P : : cos PZ : cos ZP o 
that is, rad : cos dec.; ] tan lat. : cos ZPo 
which, converted into time, gives the time from the 
star's being on the meridian ; the latter therefore being 
supposed known, the former is readily determined. 

Problem VI. 

Given the right ascension and declination of a heavenly 
body, and the obliquity of the ecliptic, to find its latitude 
and 'longitude. 

75. Let s (fig. 27) be the body, VC the ecliptic, VQ ^^ ^^^^^j 
the equator, the angle QVC denoting the given angle mine the 
of the obliquity of the ecliptic; let sV be joined by latitude and 
the arc of a great circle s V, and let fall the perpendi- longitude, 
culars sp, s r ; then it is clear, from our definitions, ^'^' ^''" 
that Vp win be the right ascension of the body s, s p 



ASTRONOMY. 



531 



Astronomy, j^g declination, V r its longitude, and s r its latitude : 
"—"V""^ we have therefore given theYp, sp, and the angle 

p V r to find V r, and ;■ s. 

Now, first in the right-angled spherical triangle 

Vp s, we have, by form 5, Table I. 

tan s p 

tan s V » := -; — — r— 

sin V p 

whence the angle sVp becomes known, and conse- 
quently also s V r, because 

sV r = sY p + pY r 
Again, 

cos V s = cos Vp . cos p s 
whence Vs also becomes known. 

Therefore, in the right-angled triangle r V s, we have 
the hypothenuse Vs, and the angle rVs to find the 
two sides V r, r s: 

which, by our form 4, Table I. are determined as 
_ follows : 

tan V r = tan V s x cos sYr = tan long, 
sin s r = sin Vs x sin sVr = sin lat. 
In like manner, the right ascension and declination 
of any body may be found, when its latitude and longi- 
tude are given ; but generally the problem is to de- 
termine the latter from the former, these being first 
ascertained from actual observation : it is tlaus the 
tables of the latitudes and longitudes have been com- 
puted. 

But as both the ecliptic and the equator are subject 
to a change in their positions, the right ascension, 
declination, latitude, and longitude of all the fixed 
stars are constantly varying, and therefore those tables 
formed for any particular epoch, will not answer cor- 
rectly after a certain time ; the annual variations, 
however, being computed, their right ascensions, &c. 
may be determined for any proposed time, as will be 
hereafter explained. 

5. Of the crepusculum, or twilight. 

Twilio-lit. 7^- The crepusculum, or twilight, is that faint 

light which is perceived before the rising of the sun, 
and after its setting. It is occasioned by the terres- 
trial atmosphere, refracting the rays of the sun^ and 
reflecting them amongst its particles. 

The depression of tlie sun below the horizon, at the 
beginning of the morning and at the end of the even- 
ing twilight, has been variously stated at different 
seasons, and by different authors ; for example, 

Alhazen observed it to be 19° 

Tycho 17° 

Rothman 24° 

Stevinus 18° 

Cassini 15° 

Riccioli, at the equinox 16° 

summer solstice . . 21° 
winter solstice . . 17|:° 
but we more commonly now in our latitudes assume 
it 18° J the same both for morning and evening and 
for all seasons of the year. 

Problem I. 

Given the latitude of the place and the suns declination, 
to find the time when tiuilight begins. 
Time when 

it com- 77. Here S denoting the place of the sun when twi- 

mences. jj y^^ begins, we have in the triangle ZPS, (fig. 28) 



ZS = 90° + 18° = 108°, the co-latitude ZP, and Plane 
the co-declination PS, to find the hour angle ZPS from f-^'^'-o Pomy. 
apparent noon. "^ '~ 

Having thus the three sides, the angle required may 
be found bv our ,5th form. Table II. ; that is, assum- 
ing ZP -I- "ZS -h PS = s 

T r7T>o /si" 2 *• sin (I s — ZS) 

i cos ZPS = A / • r^r^-^^F^. 

^ V SHi ZP sm PS 

Whence the angle ZPS may be determined, and con- 
sequently the time from apparent noon. 

Problem II. 

Given the latitude of the place to find the time and dura- 
tion of the shortest twilight. 

78. Let P fig. 28, denote the pole, Z the zenith of the Time of 
observer, S the sun, 18° below the horizon ZS = 90° f^°yT. 
+ 18° = 108°, or more generally, = 90° + 2a, '^'^"'S'^'^' 
where we suppose the twilight to begin when the sun 
is 2a degrees below the horizon ; or that the observer 
whose zenith is Z, will then see the commencement 
of the morning twilight. 

Now in consequence of the diurnal rotation, the 
declination circle PS, turning about the axis will bring 
the sun from S to S', in the horizon, or which is the 
same, the zenith Z will approach nearer to S, by de- 
scribing about P the little circle Z vi h Q, such that the 
distances Zm, 'Pm,Fb, PQ are all equal. 

When, therefore, the zenith shall have descended 
from Z to any point m, such that mS = 90°, the sun 
will appear at 90° from the zenith, the day will com- 
mence and the twilight terminate. And the arc Zm 
of the small circle will be the measure of the angle 
ZP»i, and consequently, of the duration of the 
twilight. 

In order to determine this angle, draw the arc ZBm 
of a great circle, and to its middle B the perpendicular 
arc PB, then will 

• T rjTi • ryTjT, sin i Zm sin i Zm 

sm i ZPm = sm ZPB = — t^^^t^- = ^^ 

sm PZ cos lat. 

now in the spherical triangle Z m S, we have 
Sm + mZ 7 ZS, or 
90° -h mZ 7 90° -f- 2 a 
consequently, ?n Z 7 2 a and ^ mZ 7 a 
Let ^ mZ = a + x 

then, 
. ^ „^ sin (a + x) sin a cos x -f sin r cos a 

sm I ZP??i = 1— — = r-T 

^ cos lat. cos lat. 

sin a + cos a sin x — 2 sin a sin ^^'x 
cos lat. 
because, 1 — cos x =: 2 sin "5 x (See Trigonometry) 
Now the last expression is equivalent to 

sin a . 2 sin 5 x (cos a + ^x) 
cos lat. 



sin i ZPm 



+ ■ 



cos lat. 

And here 5 .r is essentially positive, and a and | x small 
angles, such that a + ^ x /. 90°. Whence the latter 
part of the expression will be positive, and we shall 
have 

sin a 

sin I ZPm 7 :— 

^ cos lat. 

It is further evident that the twilight will be longer 
as X is greater, and shorter as .r is less, and that it 



532 



ASTRONOMY. 



Astronomy, will be the shortest possible when x is zero, because 
^— V"— ^ in that case, the second member of the second side of 
the equation will vanish. 

But this is what occurs when the triangle Z??!S is 
reduced to the arc ZS, that is, when the point m falls 
on h, or when the distance PS is such, that the part 
Zfc, of the vertical ZS, lying within the small circle 
Z??iQ is equal to 2a, and the exterior part iS = 90°. 
It is also manifest, that if PS increases, the opposite 
angle PZS will in like manner increase, and tliat on 
the contrary that angle wiU diminish as PS diminishes. 
In these variations, the point m will approach to or re- 
cede from Z, the intercepted part 6Z will vary between 
the limits and ZQ=2 PZ. Thus the intercepted part 
may have all values from to 2 (90° — lat.) = 180° 
— 2 lat. and consequently may have the value 2 a : 
hence in the case where Tib = ra, and fcS = 90°, the 
shortest twilight will obtain ; and the semi duration in 
degrees will be found by means of the equation 

. r,^-^ sin a 

sm ZPB = — = sm a sec lat. 

cos lat. 

Whence the duration in time is readily determined. 

79. Other theorems are deducible from the same 

construction and investigations ; for on the arc Z6 = 

2 a, and with the complement of ZP of the latitude 

Fig. 29. constitute the isosceles triangle ZP6, (fig. 29) and let 
fall the perpendicular Ym ; then ZP6 will be the angle 
which measures the duration. Prolong Z6, till 6S := 
90°, and draw the arc PS which will be the sun's 
co-declination for the day of the shortest twilight. 

Sun's azi- Now, 

jnuth. _, cos PZ cos PS 

cos WiP 



cos Z; 



cos m S 



"Wherefore, 



cos Zm '. cos r)iS \ \ cos PZ : cos PS 

cos a '. cos (90° + a) * sin lat. '. sin dec. 

cos a '. — sin a ; ' sin lat. '. sin dec. 



whence, sin dec. 



— sui a 



'■ sin lat. = — tan a. sin lat . 



Again, in the right angled triangle ZP»j, we have 

tan Z)H= cos Z tan PZ 
and cos Z = tan Zm cot PZ = tan a. tan lat. 

Now the angle Z or PZ»i is the sun's azimuth at the 
commencement of the twilight, and 

PZ6 = VIZ = 180° - FbS 
13ut P6S is the sun's azimuth at the instant, when his 
-centre is upon the rational, horizon ; wherefore the 
sun's azimuth at the hcginning and ending of the twilight 
are supplements to each other on the day of the shortest 
twilight, 

Hence, since cos PZS = tan a. tan lat. 
we have cos P6S = — tan «. tan lat. 

80. In like manner ZbS and 6PS are the hour angles, 
' at the beginning and end of the twilight ; let the for- 
mer be denoted byP' and the latter by P ; then 

ZPS — fePS = P' - P = ZP6 
which is the angle that measures the duration of twi- 
light. Hence we have from what has been done 
above 



sin i (P' - P) 



sin lat. 



Also, 

mPS = tPS + mVb = P + i(P'-P)=^ ^'^ + P) 

and 



sin ??!PS = 



that is. 



sin Sm 
"^nPS 
sin § (F 



sin (90° -f- a) 
cos dec. 

cos a 



cos a 
cos dec. 



+ P) 



cos dec. 

cos a 

cos dec. 

sin a 



Whence from the two equations, 
sin 1 (P' - P) 

sin i (F + P) 

^ ^ '^ cos lat. 

the hour angles P' and P are easily determined, the 
declination itself being given by the equation 

sin dec = — tan a. sin lat. 
We have also, 

sin lat. 

cos PSZ = 

cos dec. 

Lastly, let ST = 2a = Zi ; and draw PT, then ZT 
= 90°, and T is a point in the horizon for the moment 
when the zenith was in Z. Whence the triangle PZT 
gives 

cos PT = cos Z sin PZ sin ZT -|- cos PZ cos ZT 
= cos Z sin PZ = tan a. tan lat. cos lat. 
= tan a. sin lat. = sin dec. 
"Therefore, 90° — PT = dec, or PT = 90°— dec. 
But PS = 90° + dec. 

therefore, PT -h PS = 180° 

which is another remarkable property of the shortest 
twilight. 

81. In all the above deductions, the latitude has 
been left general, or indeterminate, as has .also the 
quantity 2 a, which denotes t'ne number of degrees 
that the sun is below the horizon when the twilight 
begins. The latitude may therefore be introduced for 
any given place, as may also 2 a ; but commonly, we 
assume 2« = 18°, that is, the twilight is supposed to 
commence when the sun is 18° below the horizon. 

ExABiPLE. Required the day on which the twilight Example, 
is the shortest at Woolwich, the latitude of which is 
.51° 28' AO", in the year 1820, with its duration, and 
the time of its beginning and end. 

First, for the declination we have 

sin dec. = — tan a sin lat. 
Now log tan a =9° = 9-1997195 

log sin lat. or 51° 28'4= 9-8934104 



log sin dec. = — 7° 



9-0931229 



The declination, therefore, is 7° 7' 5" south, which 
answers to March 2 and October 11. 
Again, for the duration, we have 

sini(F-P) = 



cos lat. 
= 9-1943324 
= 9-7943613 



-3999711 



from log sin 9° 
takelogcos51°26 

log sin 14° 32' 41'' 

Whence P' - P = 29° 5' 22" 

41so sin i (P' + P) = ■ ^°Y 

2 V cos dec. 



Hence 



from cos 9° = 9.9946199 
take cos 7° 7' 5" = 9.9966399 



95° 31' 19" 9.9979800 



ASTRONOMY. 



533 



Astronomy. 



whence P' + P = 191° 2' 38'' 
P'_P= 29 5 22 



2)220 8 

half sum = 1 10 - 4 = angle P' 

half dif. = 80 58 — 38 = angle P 

h m s 
The former in time answers to 7 20 IG^ 
and the latter to 5 23 54| 



between 
mean and 
apparent 
time. 



The former showing the time when the evening twi- 
light ends, and the latter the time of the sun's setting, 
or the time of its beginning ; consequently their dif- 
ference, Ih. 56m. 21§s., is the duration. 

The above numbers, taken respectively from 12, 
will leave the time of the beginning and end of the 
morning twilight. 

Distinction 82. In all the preceding investigations, we have 
considered only apparent time ; that is, we have sup- 
posed it to be 12 o'clock when the sun is on the me- 
ridian, and that it is exactly 24 hours in passing from 
one meridian to the same again ; but if a clock be 
adjusted to go thus for one day, that is, if it show 
exactly 24 hours between the time of the sun being 
twice successively in the same place, it will not con- 
tinue to show 12 o'clock every day when the sun 
comes to the meridian, because the intervals of time 
from the sun's leaving a meridian to his return to it 
again, are not always equal. This diiference between 
the sun and a well regulated clock is called the equa- 
tion of time, which will be treated of in a subse- 
quent chapter ; at present, we shall not enter farther 
upon the subject, it is suificient to apprize the reader 
that the time as determined in all the preceding pro- 
blems, is what is called apparent time, or the time 
shown by the sun, and not mean or true time, which is 
that shown by a well regulated clock. 

Corrections 83. Beside this correction for the time, there are 



for paral- 
lax, &c. 



also other corrections which must be introduced into 
the data of the preceding examples, in order to render 
the results perfectly conformable with observation. 
Thus we have all along supposed the body to rise as 
soon as it is found in the rational horizon ; but all 
bodies in the heavens, when in or near the horizon, 
are elevated 33' by refraction above their true places ; 
this, therefore, would make them appear when they 
are actually 33' below the horizon, or when they are 
90° 33' from the zenith ; and all the way from the 
horizon to the zenith refraction has the effect of ele- 
vating the apparent places of the heavenly bodies, 
but in a less degree as the altitude is greater ; till it 
-vanishes in the zenith. The altitudes, therefore, as 
we have given them, are supposed to have been sub- 
jected to these corrections, the method of making 
which will be explained hereafter. This is one of the 
principal corrections for the fixed stars ; but for the 
sun or any other of the bodies of our systein, a differ- 
ent correction becomes necessary, these being all de- 
pressed below their true places by the effect of paral- 
lax, as will also be explained in a subsequent chapter ; 
that is, we have confounded the sensible and rational 
horizon, which is admissible as far as relates to the 
fixed stars, in consequence of their immense distance; 
but the angle subtended by them or by the earth's 
radius, at any of the bodies of our system, is a sensi- 

VOL. III. 



ble quantity that must not be neglected in any compu- Plane 
tations relative to such bodies. The parallax has Astronomy, 
therefore a tendency to increase the apparent zenith ^— '"v'— ^ 
distance of any body in our system, wliile the refrac- 
tion tends to diminish it ; therefore the actual zenith 
distance of a body when it first becomes visible to a 
spectator on the earth, is equal to 90° — hor. parallax 
+ refraction. 

84. What has been hitherto done, has been merely 
to indicate the nature of the calculations after certain 
observations have been made and corrected ; we now 
propose to explain the instruments used for making 
these observations, the method of employing them for 
these purposes, and the nature and quantity of the 
corrections that are requisite for reducing the results 
thus obtained, so as to render them proper for the 
purposes of astronomical computation. 

§ IV, Description and use of the most indispensable as- 
tronomical instruments. 

85. _ We shall not attempt in this place a general Astronomi- 
description of astronomical instruments, this will cal instru- 
be given under a distinct head in another part ments. 
of this work; our purpose here is only to describe 
those whose use is indispensable in the pursuit of 
this science, and with the principle of whose con- 
struction and operation, it is essential that the student 
b*e well informed, if he wish to proceed upon any 
other data than those furnished by the report of other 
observers. 

1. Of the astronomical telescope. 

86. We have already in our treatise on Optics de- Astronomi- 
scribed and illustrated the principles of this instru- cal teles- 
ment, we have therefore in this place merely to speak ^°'S^- 
of its application to astronomical observations. 

Let, then, AB (fig. 30) represent the diameter of Fig. 30. 
any heavenly body, as the sun, moon, or planet ; m 
its middle point, will send out a luminous pencil of 
rays, which by means of the refraction of the lenses 
will be imited in the focus of the telescope. The 
same will be the case with all the points of the disc, 
and an image of the object GH will be formed, as we 
have already explained in our treatise on Optics; 
H being the image of the point B, and G of the point 
A ; that is, the image will be reversed with respect to 
its actual position. The motion of the object is also 
reversed, so that if it moves from left to right in the 
heavens, it will move from right to left in the tele- 
scope ; but the effect being the same for all bodies, 
there Avill result from it no practical inconvenience ; 
it is suflSicient that we are apprized of it. 

Let us farther observe, that the angle HeG = ACB, 
and if the focal distance eF is to the breadth HG in 
such a ratio that 

i^ = tan|ACB 

the object will be shown entire in the telescope ; but 
if the focal distance be efj CF, the image hg, will be 
larger than the field of the telescope, and consequently, 
we shall not then see it entire. On the contrary, if 
the focal distance be CQ, less than CF, the image 
h'Qg' will not fill the telescope. 

Generally, the field of the telescope is found by the 
3 z 



I 



534 



ASTRONOMY. 



Astronomy, formula 
^""^ "^ tan I field : 

tan i field = 



diam. of the tube 
focal length 

i diam. of the tube 



Use of tlie 
cross wires 
Fig. 31. 



radius of curvature of the object glass 
Or in case of a diaphragm being placed in the tube, as 
is commonly practised to prevent the reflection of the 
oblique rays, then 

T ^ , , I diam. diaphrasnni 
tan § field = S — 7 — , . \. ^ 

^ focal length 

These results, which are immediately deducible from 
what has been done in the preceding treatise, are stated 
here merely for the sake of avoiding frequent refer- 
ences to those articles ; with the same view we may 
state the following relative to the magnifying power 
of such an instrument as we are here speaking of, 
viz. 

focal distance obj. glass 

magnirv-ing power = 7 — t—-. — = 

^^ ■' °^ focal distance eye glass 

By which is to be understood, that the angle under 
which we view the image is equal to that under 
which we should see the object if it were brought so 
manv times nearer as is indicated by the above 
fraction. 

Having said thus much with regard to the teles- 
cope more commonly employed in astronomical ob- 
servations, let us offer a few remarks relative to the 
apparatus attached to it, for rendering those observa- 
tions more precise than they could be obtained with 
this instrument in the simple state in vshich it has 
been described above. 

S*. Of the reticule or cross wires. — Let ABDF (fig.31) 
represent a section of the telescopic tube or of the 
diaphragm with which it is furnished. On the edges 
of this ring or circle, are attached with two screws a 
metallic thread or fine wire DF ; this is in a transit 
instrument called the horizontal wire. Perpendicular 
to this thread are placed five others ; the centre one 
AB bisecting DF in C, and the other four at equal dis- 
tances, two on each side of AB. 

A star or any other heavenly body passes the field 
of view of a telescope in different times according to 
the diameter of the instrument, and the polar distance 
of the body ; therefore, if the telescope were iinpro- 
vided with some such an apparatus as here described, 
it would be difficult or even impossible to say precisely 
the moment when it was in the axis or in the centre 
of the instrument, and the accuracy of modern science 
requires this determination to the utmost accuracy : 
let us see what precision is attainable by means of the 
cross wires above indicated. 

The point C or G being supposed either in the cen- 
tre of DF, or in the vertical line bisecting DF, at the 
moment a star passes it, if the diameter of the thread 
be equal to that of the star, it will be entirely hidden 
by it, and that moment v\-ill be the time of its passage : 
but more commonly the thread is sufficiently fine, thct 
at the instant of passage, it will bisect the star, an 
equal portion of the latter being observable on each 
side of the former ; and thus the time of passage 
might be found to within one-fourth or one-fifth of a 
second. But it is obvious that we may observe the 
same with respect to all the other four vertical wires, 
which being at equal distances, the times of passing 



each in succession from the first ^vill form an arith- piane 
metical progression ; and by taking the mean of the Astronomy, 
five, we shall have the time of the star passing the *•— v'-w^ 
centre wire still more exactly, and by this means, we 
may generally depend upon our observation to wdthin 
one-tenth of a second. 

Our figure and the description of it, applies to the 
case of an instrument fi_\ed in the plane of the meri- 
dian, in which case the motion of a heavenly body 
wiU be apparently horizontal. In any other case, the 
star ascends or descends obliquely, and then it is ne- 
cessary to give to the wire DF, a similar inclination, 
so that the motion of the star may be parallel to it, as 
in the line ES, as shown in fig. 32, the proper apparatus Fig. 32. 
being supplied for this purpose. The only difficulty 
of observation is when the night is very dark, and 
when we are unable to see the threads except for the 
moment when the star is bisected by them : which 
being almost instantaneous, we are not suihciently 
prepared for noting the time. In order to obviate this 
difficulty, the interior of the tube is illuminated by 
the following apparatus. 

SS. In the side of the tube of the telescope, and Method of 
commonly in the axis on which it turns, is made a f'^'='|t«'i- 
small hole, directly opposite to which is placed, in the {°|g^ ^ 
tube, a small mirror, inclined to the axis or sides of 
the telescope, at an angle of 45°. The light of a small 
lamp falls on the mirror, and forming with it an angle 
of 45°, it is reflected at the same angle, and therefore 
passes in a line parallel to the axis of the instrument, 
and thus renders tiie wires sufficiently visible. If the 
star on which the observation is made be of the 9th 
or 10th magnitude, we must however be careful to 
modify the intensity of the illumination, as otherwise, 
the artificial light will render the natural light of the 
star imperceptible, and it will be in danger of passing 
unobserved. 

S9. At present we have spoken only of the transit Obserra- 
of a fixed star, if it be the sun or moon that we are tions on the 
observing, we must ascertain the time when their re- ^"^ °^ 
spective centres pass the axis of the instrument. For ™°**°* 
this purpose we note very accurately, the instant 
when the eastern or western limb comes in contact 
with each of the five wires in succession, and the sum 
of the times divided by 5, will be the instant- when 
that limb passed the centre wire. These five obser- 
vations being made, the other Umb of the sun or moon 
will be just about leaving the first wire, we therefore, 
in like manner, note these other five instants, the 
mean of which will give the time when the last limb 
passed the centre wire, and the mean of the two will 
be the time of the transit of the centre. 

90. Having said thus much with reference to the 
telescope and the apparatus with which it is supplied, 
it remains for us to describe the instruments to which 
it is attached, and the nature of their adjustment ; for 
the accuracy of observations indicated above with 
reference to the object traversing the axis of the tele- 
scope would be to little purpose, unless we could be 
equally precise in the determination of the direction 
of that axis, both as regards the horizontal and verti- 
cal position of the instrument. 

By^far the greater number of astronomical obser- 
vations are made in the plane of the meridian ; but 
some are made at different azimuths, and different in- 
struments are best employed for these purposes ; at 



ASTRONOMY. 



535 



Astronomy, the same time some are so constructed as to answer in 
^-"—y-^^ both cases ; at present we sliall confine our explana- 
tion to only one of the most perfect of each sort, but 
in a future part we shall enter upon the subject more 
at length, and endeavour to illustrate the advantages 
and defects of different constructions. 

Of astronomical quadrants. 
■91. These may be either portable or fixed ; in the 
former case tliey are commonly mounted on a tripod, 
and may be used for taking altitudes in any azimuth, 
or be made to follow the body observed in its apparent 
path ; but in the latter case, the instrument is fixed 
in the plane of the meridian against a substantial wall, 
and is hence denominated a mural quadrant. 

2. Portable astronomical quadrant. 

Portable as- ^2. The great variety of forms under which this 
tronomical instrument has appeared, the numerous methods pro- 
quadrant, posed by diiferent artists for adjusting it to its verti- 
cality, &c. would be sufficient of themselves, -were we 
to enter at length upon the subject, to form a consi- 
derable volume ; we shall, therefore, select one of 
those esteemed the most perfect, and limit ourselves to 
the description of that only ; which will be amply 
sufficient for our present purpose. 
Fig. 33. Fig. 33 represents a portable quadrant, constructed 

by Ramsden for the observatory of Christ's College, 
Cambridge. The tripod on which it is mounted has 
screws of adjustment to set the stem, on which the 
horizontal miotion is performed, perpendicular, which 
is proved to be so in all directions when the plumb- 
line bisects both the superior and inferior dots during 
the whole revolution in a horizontal circle. The vi- 
sible stem is a brass tube, and through it ascends a 
solid steel vertical axis, which fitting closely at the 
upper and lower extremity, has not the least shake, 
and preserves the position once given to it, so long as 
the feet screws are unmolested. The telescope is of 
the achromatic construction, and has the usual appa- 
ratus for a slow motion. The telescope lies on a bar 
tliat carries the counterpoise, and in which is the cen- 
tre of its motion. It has a system of wires in the 
focus of the eye glass, which are adjustable by screws 
both upwards and sideways, as well as in a circular 
direction, so that the adjustments for coUimation, and 
for zero in the altitude of the circle, may be thereby 
effected. The point of suspension of the plumb-line 
is also adjustable by a proper screw apparatus. At 
the top of the vertical tube or stem, is a small hori- 
zontal circle with a clamping apparatus for slow hori- 
zontal motion, by means of which the whole quadrant 
with its attached telescope turns gradually round in 
azimuth. When the observation is made in or near 
the zenith, the plumb-line of this instrument falls in 
the way of the telescope, and is obliged to be removed. 
This, however, is supplied by the addition of a spirit 
level, suspended from an adjustable horizontal brass 
rod, under the uppermost radical bar of the quadrant, 
which level not only supplies the place of the plumb- 
line when taken off, but at all times serves as a check 
on its adjustment, and when furnished with a gradu- 
ated scale, may very well be made its substitute. We 
shall not here attempt to describe the nature and di- 
vision of the vernier scale, it will be sufficient to ob- 
serve, that the angles may be ascertained to the lOths 



of seconds. We proceed next to the adjustments of Plane 
the instrument. Astronomy. 



To adjust the axis of the pedestal vertical. 

93. This adjustment may be performed either by the Adjustment 
plumb-line or by the level. When the plumb-line is °^ ^''^ ^'^' 
used, turn the quadrant in azimuth till its plane, or s''""™^"* '» 
which is the same thing, till the telescope lies parallel ^ ' "^'^ 

to a line joining any two of its three feet, and turn 
one of the two screws of the feet till the wire bisects 
the lower dot, and with the proper screw bring the 
upper dot to the same wire ; then reverse the tele- 
scope by turning 180° in azimuth, and if both dots 
are again bisected, the axis is vertical in the direction 
that the telescope has pointed ; in the next place, turn 
the telescope the space of a quadrant till it points in 
the same direction as the third foot of the tripod, and 
make the wire bisect the lower dot by the screw of 
this foot, and it will be found to bisect the upper dot 
also, if the first adjustment was properly made, but 
if not, repeat the operation till both dots are bisected 
in all the reversed situations of the telescope, and 
then the axis will be vertical in every direction. 

In making this adjustment by the level alone, 
the process must be thus ; first, the level must be 
made parallel to the rod Avhicli it hangs on, and se- 
condly, this rod must be put perfectly horizontal, and 
the level will be horizontal also, with the bubble in 
the middle. In order to make the level parallel to 
the rod, place it parallel to a line joining two of the 
feet screws, and bring the bubble to the middle by 
one of the feet screws in question ; then take off and 
reverse the position of the level, and if the bubble is 
found in the middle now, tl:ie parallelism is perfect ; if 
not, one half of the error must be rectified by the 
same foot screw, and the other half by the adjusting 
screws at the end of the rod, by releasing one and 
screwing up the other. A repetition or two of this 
process will make the bubble stand in the middle in 
both of the reversed situations. In the next place, 
with the level thus parallel to the rod of suspension, 
turn tlie quadrant round its axis an entire semicircle 
as nearly as can be estimated, and if the bubble will 
now rest in the middle, the rod is level, and being at 
right angles with the axis of the quadrant's motion, 
proves that this axis is vertical in every direction ; 
but if the bubble be found to run to one end of the 
tube, bring it one half way back by the adjusting 
screws of the rod, releasing one and fixing the other, 
as the case may require, and the other half by the 
proper foot screw. A repetition of this process will 
soon settle the bubble in the middle during a whole 
revolution in azimuth, and then the adjustment of the 
axis is perfect, as well as of the rod and level. 

94. The second adjustment is that by which the line Adjustment 
of coUimation of the telescope, is made parallel to the forcoUima- 
horizontal line that passes to the centre of the qua- *'°°' 
drant to zero on the limb, or quadrantal arc, at 

the same time that zero on the vernier coincides 
with zero on the limb. This important adjustment 
may be made in several ways, some of which are 
tedious and otherwise objectionable ; but we shall 
confine ourselves to two, which apply one to the ver- 
tical, and the other to the horizontal line of the qua- 
drant, which two methods, when duly effected, will 
not only check each other, but detect the error of 
3 z 2 



I 



536 



ASTRONOMY. 



Astronomy, the total arc, if there be any at the same time ; which 
V_-.y—i »^ is an acquisition of the utmost importance. First 
then to adjust by the vertical line, let the axis of the 
quadrant be made truly perpendicular in all directions 
by tlie adjustment we have already described, and fix 
on a star within a few degrees of the zenith when 
exactly on the meridian, and measure its altitude by 
the cross wire in the field of view in the usual way, 
and note down the result ; if these readings prove to 
be at equal distances from the point 90^, one on the 
quadrant arc, and the other on the arc of excess be- 
yond 90°, the horizontal wire is truly placed in the 
eye piece, but if not, half of the difference of the 
readings must be corrected by the proper screw for 
raising or depressing the said wire. This may be 
done by directing the telescope to a distant mark till 
the cross wire bisects it, then by moving the screw of 
slow motion of the vernier the half quantity required, 
and by bringing back the cross wire tlius displaced to 
its original mark again. This operation repeated will 
place the cross wire in such situation, that zero on the 
vernier will be in its proper place with respect to the 
point 90° 5 or the half difference thus ascertained may 
remain, without altering the cross wire, as an error of 
adjustment to be constantly applied with the sign + 
or — , as the case may be, in all subsequent observa- 
tions. Again, to adjust by the horizontal line passing 
through the zero of the quadrantal arc, it will be ne- 
cessary to have a second telescope turning on pivots 
in adjustable y's attached to the back of the quadrant, 
on the same level with the said horizontal line of the 
quadrant. This telescope may be called the adjusting 
telescope, and may be also used to watch a distant 
mark, before and after an altitude is taken, in order to 
detect any deviation in the position of the vertical 
axis that may happen during the operation of mea- 
suring. Let the adjusting telescope bisect a fine 
distant mark with its cross wire, and turn the tube of 
the telescope round one half way on its pivots, as it 
lies in a horizontal position, and if the wire now bi- 
sects the same mark it is truly fixed, if not, look out 
for a new mark a little laigher or lower, as the case 
may require, and make it cut that in the reversed po- 
sitions of the cross wire, by means of the proper screw 
for the purpose ; now this adjusting telescope will be 
adjusted for coUimation. In tlie next place, put zero 
on the vernier to zero on the limb, and direct the tele- 
scope of observation to the distant mark, by which the 
adjusting telescope had its wire adjusted, and let this 
mark be bisected by both telescopes, the level and 
plumb-line at the same time showing tliat the vertical 
axis is perpendicular ; now turn the quadrant half 
round its azimuth, and reverse tl^e adjusting telescope 
so as to view the same distant mark again, and if it be 
found to bisect it as before, the horizontal line of the 
quadrant is right, and all the quadrantal arc without 
error, supposing the telescope of observation to have 
its adjustment for collimation as fixed by the point 
90°, above described ; but if this adjustment of the 
point zero on the limb be first made, half the appa- 
rent error must be rectified by the screw at the eye 
piece by means of reversed positions and marks ; and 
then afterwards the adjustment by a new star near the 
zenith will detect the error of the whole arc. If, how- 
ever, no error in the total arc exists, then the adjust- 
ment for collimation may be made either from the 



horizontal or from the vertical measurement, as may -pi^rie 
be most convenient ; one of which is more practicable Astronomy, 
by day, and the other by night. When this delicate ^— >^^-^' 
and most essential adjustment is finally settled, the 
object glass of the telescope should not be disturbed, 
and therefore it would be adviseable to have its inte- 
rior surface well cleaned previously. It was taken for 
granted that the cross wire was perfectly horizontal 
during the time the preceding adjustment was made, 
or, which is the same thing, that the parallel wires 
were perpendicular to the horizon. This is proved in 
a simple manner thus ; direct the telescope to a fine 
small distant mark, or make the adjustment for vision, 
if necessary, then if one of the vertical wires will con- 
tinue to bisect the said mark through the whole field 
of view while the telescope is elevated or depressed, 
the wires are right, but if not, they must be made so 
by the proper screws for that purpose, near the focus 
of the eye-glas. This preparation ought to precede 
the last adjustment, and when once made, seldom 
requires altering, except in case of accidental injury. 
It has also been assumed in the preceding adjustment, 
that the maker of the instrument placed the plane of 
the quadrant parallel to the axis of its motion, and 
also its line of collimation of the telescope parallel to 
the said plane. The former may be known to be true 
thus : if, when the plumb-line is adjusted at its centre 
of suspension, just to escape touching the limb (which 
should always be the case) the motion of the quadrant 
in azimuth will not alter it in this respect, the plane 
is truly fixed ; but if not, the screws that fix the qua- 
drant to its axis must be resorted to for its alteration, 
which is best done by the maker. When there is no 
plumb-line, a small spirit level fixed at right angles 
to the plane of the quadrant will answer the same pur- 
pose ; for the resting of the bubble during the qua- 
drant's revolution in azimuth, A^ill be a proof that 
the plane to which it is at right angles is vertical. 
With respect to the parallel position of the telescope, 
as this is guided by the vernier sliding on the limb, it 
is the business of the maker to adjust it properly, 
which he will best do by a comparison with a good 
transit instrument of the passages of a high and of a 
low star in each of the two instruments, but a small 
deviation of the telescope witli respect to parallelism, 
though to be avoided, if practicable, will not sensibly 
affect the measurement of altitudes, which is the sole 
business of this instrument. If, however, tliis devia- 
tion be considerable, the eye end of the telescope must 
be set nearer to or farther from the limb, as the case 
may require, by the maker himself. We have been 
the more minute in describing these adjustments, not 
only because they are indispensably necessary in 
making good observations, but because they will 
applv, one or other of them, by means of the plumb- 
line or of the spirit level, to all other astronomical 
quadrants that have. a motion in azimuth. 

3. Of the transit instrument. 
95. Transit instruments, as they are now con- Transit in- 
structed, may be considered either as fixed or port- strument. 
able ; the former of which was the original construc- 
tion, and is still that commonly made use of in 
permanent observatories , for the purpose of determining 
in conjunction with a good astronomical clock, the 
right ascensions of the heavenly bodies ; but the latter 



ASTRONOMY. 



i37 



Fig. 34. 



Astronomy, may be used in any place for asoei-talning the rate of a 

v*--^^— «-^ clock or chronometer, and when nicely brought into 

the meridian, for determining also the right ascension 

with considerable accuracy. It is one of the latter 

only that we proposed to describe in this place. 

The best construction of a portable transit instru- 
ment, is that represented in our lig-. 34, where are 
shown all the parts that are necessary to be described 
under this article. This instrument is one of tlie 
numerous inventions of Troughton, and by no means 
one of the least useful. 

The telescope of this transit is 20 inches in length, 
and magnifies from 20 to 3.5 times, according to the 
eye pieces that are employed ; two of which are 
usually of the prismatic or diagonal kind, to be used 
at considerable altitucks : the aperture is 1| inches, 
and the power is sufficient to enable us to see the 
pole star by clear day light. The base of the instru- 
ment is a thick ring or rim of brass, which receives 
three equidistant screws for feet, besides the four 
screws that fix the two vertical frames to the base, 
and which constitute the supports of the axis ; one of 
these is shown complete in the first of our two figures. 
These supports are kept perpendicular by the interior 
bracing bars, of which two are seen in the second 
figure ; they are attached by thumb screws at both 
ends to the base and upright frames respectively. The 
circular figure of the base is not only firm, but pre- 
serves its shape in all degrees of temperature ; and 
when the parts are detached, by loosening the thumb 
screws, the whole pack into a box, which is of conve- 
nient size for carriage ; the diameter of the circular 
base, and the consequent length of the axis, is a foot 
within, and the height of the supports thirteen inches. 
The graduated circle being of six inches diameter, 
admits of reading by each of the two opposite verniers 
to minutes, which is sufficient for finding the meri- 
dian altitude of any celestial body of which the decli- 
nation is known, when the latitude is given ; or for 
determining the latitude when unknown, to the accu- 
racy of the nearest minute. 

If the circle were made a little larger, and three 
verniers substituted for the two, a longer level might 
be used, and the readings made accurate to 20" or 
30''' ; but as the intention of the inventor was not to 
make it an altitude instrument, he has limited himself 
only to such conditions as were requisite for consti- 
tuting an useful transit instrument in a portable form. 
The level of this transit is wholly detached, is equal 
in length to the axis itself j and is intended to be 
placed over the same, by restingupon it, having notches 
on its end pieces, which become tangents to the 
cylindrical parts of the axis or pivot ; so that the re- 
version is performed without any inconvenience : but 
it is necessary to remove the level when the altitudes 
are great, in order to avoid its being displaced and 
broken by any alteration in the elevation of the tele- 
scope. There are usually three studs of brass in- 
cluded, with the darkening glasses, lantern, and other 
appendages ; two of which studs have conical holes to 
receive the points of the screws or feet of the circular 
base ; and for this purpose all the studs must be made 
fast to the slab or pillar which supports the instru- 
ment, by plaster of Paris orputty, inserted into as many 
holes in the plane of the marble or stone, care being 
taken that the line which joins the two conical points 



be in the direction of the meridian, or so nearly so, Plime 
tiiat the adjusting screws of one of the Y's will bring Astroiwrny. 
it into that situation. ^— "-v"— ^ 

Mr. Jones, of Charing-cross, has made several 30 
and 42 inch transit instruments of the j)ortable sort, 
supported by oblong frames of cast iron, which look 
neat, and answer the purpose very well. These have 
all the advantages of the instrument last described, 
and at the same time of course have greater powers 
in tlie telescope, and are cheaper in i)roportion to 
their size. He has also made some with telescopes of 
only 20 inches, for the sake of being more portable. 

Of the adjustments. 
1. Of the level. 
^Vhen the level hangs on, or is made fast to the 
axis, put the telescope in its place, and observe to 
whicli end of the level the bubble runs, which will 
always be tlie more elevated end ; bring it back to 
the middle by the Y screw for vertical motion, or by 
the foot screw under the end of the axis, and then in- 
^'ert the axis end for end ; then, if the bubble is again 
found in the middle, the level is already parallel to 
the axis ; but if not, adjust one half of the error by 
the adjusting screw of the level, and the other half 
by the Y screw, or that at the foot of the support, 
and let the operation of reversing and adjusting by 
halves be repeated until the bubble will remain sta- 
tionary in either position of the axis, in which case 
the level will be right. When the detached level is 
used, that notch must be made a little deeper wher« 
the bubble is, by scraping it with a penknife, instead 
of using an adjusting screw, with which it is not 
commonly provided. And when the notches whicli 
rest on the pivots are once made right, they will sel- 
dom require a second rectification. 

2. To place the axis of the telescope horizontal. 
If the spirit level be made use of, the same opera- 
tion which we have just described, will put the axis 
level, at the same time that it brings the level parallel 
to the axis ; for unless both these conditions be ful- 
filled, the adjustment of the level will be deranged 
by reversion ; and when this is not the case, it is a 
proof that both the level and the axis are truly hori- 
zontal. Hence, when the level is previously adjust- 
ed, it will be sufficient to bring the bubble to the 
middle of the level, by the Y screw, or the foot screw 
alone, as the construction may require. 

It is not necessary for our present purpose to de- 
scribe the adjustments of the larger instruments, but 
we may just observe, that when in these the plumb 
line is employed, it is applied to a frame suspended 
by the pivots of the axis, that will reverse in position 
according to Ramsden's method, or hanging on the 
tube of the telescope parallel to the line of collima- 
tion ; in either case a dot is bisected by the plumb- 
line near the point of suspension, and another near 
the lower end of the line, in both the reversed posi- 
tions of the axis, when the adjustment is truly made 
by the proper screws as above directed. 
3. To adjust the telescope. 
That is, to place an eye-glass and object-glass at 
such a distance from each other, that their respective 
foci may coincide : after which, the wires are to be 
brought into their common focus. To effect this. 



538 



ASTRONOMY 



Astronomy, some telescopes have the eye-glass and cell, which 
^— 'V"^ carries the wires, moveable, while the object-glass is 
fixed : others have the wires fixed, and the two glasses 
moveable. In the former case, by pushing in or 
drawing out the eye piece, adjust the telescope so that 
the sun or a planet appears perfectly distinct through 
it J then move the wires nearer to, or farther from, 
the eye-glass, as may be required, until they also 
appear perfectly distinct, and the telescope will be 
adjusted ready for use. In the latter construction, 
push in, or draw out, the eye piece, till the wires ap- 
pear perfectly distinct ; then alter the object-glass 
until the sun, or a planet, appears perfectly distinct 
also, and the telescope will be adjusted ready for use. 
As it is of importance to have the telescope adjusted 
very exactly in this respect, the following method of 
trying whether it be so or not, may be practised. 

The telescope being adjusted to distinct vision for 
distant objects, when a fixed star is on the meridian, 
bring the horizontal wire to bisect it very exactly, and 
the star will run along the wire through the whole ex- 
tent of the field of the telescope. While the star Is thus 
running along the wire, move your eye a little upward 
or downward ; and if the wires be not exactly in the 
common focus of the two glasses, the star will appear 
to quit the wire when the eye is moved. If this be the 
case, the wires or glasses must be altered until the star 
will not quit tlie wire by the motion of the eye ; the 
objects appearing perfectly distinct at the same time. 

To bring a transit instrument into the plane of the 
meridian. 

Take the altitude of the sun, noting the times by 
* the watch or clock, and thence find the apparent time, 
the latitude of the place, and the sun's declination 
being known. The difference between this time and 
the mean of the times shown by the watch when the 
observations were made, will be what the watch is 
too fast or too slow, for apparent time. 

If the watch is too fast, add the difference to 11 
hours : but if it be too slow, subtract it from 12 hours, 
and you will have the time by the watch when the 
sun will be on the meridian, as near as the going of 
the watch can be depended upon. Take the time 
which the sun's semidiameter is in passing the meri- 
dian from the Nautical Almanack, and add it to, and 
subtract it from the time by the watch, when the 
sun will be on the meridian, and you will have the 
times when the sun's eastern and western limbs will 
be on the meridian. A few minutes before the time 
when the western limb will be on the meridian, let 
your assistant count the seconds as they pass, by the 
watch j but instead of calling the 60th second, let 
him name the minute the watch is then at. While he 
is doing this, you must bring the sun into the teles- 
cope by elevating it to the proper altitude ; and turn- 
ing the whole instrument round on the screw pin U. 
Having by this means brought the middle wire appa- 
rently to the eastward of what appears to be the 
eastern limb of the sun, (because the sun will appear 
to move that way in the telescope) tighten the screw 
U by turning the nut ; and when the sun's limb arrives 
at the middle wire, keep it on it by turning the screw 
g, at the rate the sun moves, till your assistant calls 
the second by the watch at which you had computed 
the western limb of the sun would be on. the meridian : 



and the instrument will be nearly in the meridian, piane 
Let your assistant count on till the watch arrives at Astronomy, 
the second, when, according to your calculation, the ^^— -^-^^ 
eastern limb of the sun should be on the meridian ; 
and, if it is not exactly on it, you will have another 
opportunity of rectifying the instrument by turning 
the screw g. 

Having thus brought the instrument into, or very 
near the meridian, its real situation with respect to 
the meridian may be verified several ways ; of which 
we shall point out two. If the latitude of the place 
be considerable, that is, 30 degrees or upward, there 
are a variety of stars in both hemispheres sufficiently 
bright, which never set : and consequently, they may 
be observed with the instrument both above and below 
the pole. 

Let the transits of such a star over the meridian be 
observed above and below the pole; and it is mani- 
fest, that if the time of the first transit above the pole 
be subtracted from the time of the second transit 
above the pole (adding 24 hours if necessary), the 
remainder will be the time by the watch, in which the 
earth (or the star apparently) makes one diurnal revo- 
lution. It is also evident, that if the two intervals 
between the time of the transit below the pole be 
equal, the instrument must be exactly in the meridian. 
If the interval between the first transit above the pole, 
and the transit below the pole be greater than the 
interval between the transit below the pole and the 
second transit above it, the object end of the tele- 
scope, when directed toward the elevated pole, lies to 
the east of the true meridian ; but if the latter inter- 
val be greatest, the object end of the telescope, when 
directed towards the elevated pole, lies west of the 
true meridian. 

To correct the error, bring the instrument into the 
meridian ; add 24 hours to the time of the latter tran- 
sit above the pole, subtract the time of the former 
from it, and take half the remainder. Take the dif- 
ference between this and the interval between the 
transits above and below the pole, and take half this 
difference. Then, as the time by the watch of an 
entire revolution is to 24 hours, so is this half differ- 
ence to the half difference in sideral time. Add to 
the logarithm of this half difference, the logarithmic 
tangent of the star's polar distance ; and the loga- 
rithmic secant of the latitude of the place, the sum, 
rejecting 20 from the index, will be the logarithm of 
the number of seconds in time, which expresses the 
angle made by the instrument and the meridian. 

Consider what part this angle makes of the interval, 
between the wires which are in the focus of the tele- 
scope ; and turn the instrument on its axis till the 
telescope points at the horizon. Look out for some 
tolerably distant object which is cut by one of the 
wires ; and by turning the screw g, remove the wire 
to the east or west of this object (as may be re- 
quired), such a part of the space between that wire and 
the next to it, as the angular error which the instru- 
ment makes of that interval. You must then proceed 
to examine the position of the instrument again, 
either by the same, or some other circurapolar star, 
and to correct it, if it requires correction, until you 
get it exactly into the plane of the meridian ; and 
when you have, a mark must be set up in the meri- 
dian at as great a distance from the instrument as 



ASTRONOMY. 



539 



Astronomy, may be convenient^ or as it can oe seen distinctly ; 

^"■*-V"»'' and the telescope must be carefully adjusted to this 
mark before every observation. See also vol. 1 of 
the Transactions of the Astronomical Society, 

4. To adjust a clock or watch by observation. 
96. In the preceding article we have supposed the 
watch to be already regulated;, and have shown how 
from this the transit may be adjusted ; we shall now 
suppose the instrument correctly fixed, and show the 
method of adjusting the clock or watch. 
Regulation The instrument then being thus adjusted, observe 
of the clock i\^q hour, minute, second, &c. when any particular 
star traverses over the centre of the field of the teles- 
cope, by taking the mean of the times when it passes 
each wire as described (art. 87). Observe the same 
the next day, and for several days in succession, as 
also with different stars ; and if the clock be pro- 
perly adjusted to sideral time, each star ought to 
transit the meridian at the same instant every day that 
it is observed. If it marks different times on the dif- 
ferent days, it will be easy to determine from the 
mean of these observations, how much it gains or 
loses per day ; and if this error be considerable, the 
pendulum must be lengthened or shortened by the 
proper adjusting screw according as it gains or loses ; 
but if the error be not more than a fraction of a 
second, or even a second or two, and uniform for 
every equal interval of time, the pendulum may be 
allowed to remain, and the proper correction applied 
whenever any observation is made. 

We here suppose the clock to be adjusted to sideral 
time, or to register exactly 24 hours from one transit 
of any fixed star to another; if the clock be adjusted 
to mean solar time^ like those employed for common 
purposes, it ought to show only 23h.56'41''.l, which 
is the length of a sideral day in mean solar time. 
But for all the purposes of an observatory, sideral 
time is to be preferred. The clock may also be regu- 
lated by the transit of the sun ; but before we can 
employ it for this purpose, it will be necessary to 
enter at some length into an explanation of what is 
termed the equation of time. We shall therefore only 
further observe, that the best way of observing the 
transit of any heavenly body, is to watch it first into 
the telescope ; then the clock being supposed close at 
hand, note the hour, minute, and second of its en- 
trance ; and with your eye then applied to the teles- 
cope, count the beats of the pendulum till the body 
passes the first wire, and note down the exact time ; 
between the time of its passing the first and second 
wire observe again the time by the clock, and proceed 
again as before , and so on with all the wires ; and 
the mean of the several results will be the true time 
of its passing the centre wire as already explained, 
(art. 87.) ^ 

Estimation 97. The right ascension of any heavenly body is, 
of right as- as we have already observed, the arc of the equator 
cension in intercepted between the first point of aries, or that 
point where the equator is cut by the ecliptic, and the 
point where a secondary to the equator, passing through 
the body, meets the latter circle. But as the motion 
of the earth, or the apparent motion of the heavens, is 
uniform, Ave may also denote any arc of right ascen- 
sion, by the interval which elapses between the time 
when the first point of Aries passes the meridian of any 



place, and that of the transit of the proposed body. Plane 
The right ascension may be therefore estimated in Astronomy, 
-measure or time ; but the lat'er is the most common : ^'■^"v"-^ 
in the Nautical Almanack, for example, jve always 
find the sun's right ascension noted in sideral hours, 
minutes, seconds, &c. The right ascension of any 
heavenly body is then readily obtained by means of 
our clock and transit instrument ; for the former being 
set to O hours at the moment when the first point of 
Aries passes the meridian of any place ; and being 
supposed correctly adjusted to sideral time by means 
of the preceding observations, the right ascension of 
any body will be shown in time by the clock, and this, 
when requisite, may be immediately reduced to an- 
gular measure by saying, as 24 hours '. to the time 
shown by the clock ; ". 15° : to the measure sought ; 
or the reduction may be made by means of a table 
computed for the purpose. If the clock has any rate, 
that is, if it does not show correct sideral time, the 
proper correction must be applied, as indicated above ; 
and if the clock be not so adjusted as to show Oh. Om. 
Os. when the first point of Aries passes the meridian, 
then it is obvious that the difference of the two times 
will be the right ascension sought. 

It is proper, however, to make here one impor- Certain re- 
tant remark, which is, that what we have called above quisite cor- 
the first point of Aries, is not a fixed point, but that it rections. 
changes its place by a slow retrograde motion from 
year to year, called the precession of the equinoxes ; 
therefore, the right ascension of the stars is also va- 
riable, and stand in need of constant corrections ; we 
shall not, however, enter upon this subject at present, 
our purpose here was only to show how the right 
ascension of a heavenly body might be determined, 
that of any particular body being given. 

Most of the principal stars have had their right as- 
censions ascertained with the utmost precision, par- 
ticularly 36 of them, by Dr. Maskelyne;^- as well as 
their annual variations ; these, 'therefore', are now 
commonly employed by most astronomers for the pur- 
pose of regulating their clocks, and then by means of 
the clock, the right ascension of the sun, moon, and 
planets, at any time, is ascertained ; as well as that of .^, 
any fixed star, (which is supposed to be not correctly 
established,) may also be determined according to the i^. 

principles above explained. 

98. We have seen in our illustration of the circles Coy^ectio 
of the sphere, that the altitude of any body when on ^j. observ- 
the meridian will be suflicient for determining its de- ed altitudes 
clination ; for the altitude of the equator or point E 
in our fig. 22, is equal to the co-latitude ; and the dif- 
ference therefore, between the meridian altitude and 
the co-latitude of the place of observation is equal to 
the declination, which in our latitude will be north 
or south, according as the former of those quantities 
is greater or less than the latter ; and having the 
right ascension and declination, the latitude and lon- 
gitude of the body may be computed as explained in 
art. 75 ; or, on the contrary, the latitude and longi- 
tude being given, the right ascension and declination 
may be computed, the obliquity of the ecliptic being 
supposed given. But as we have before observed, the 
altitude of a body, as determined from observation, 
stands in need of certain corrections for parallax, re- 
fraction, &c. which we have not yet investigated, con- 
sequently, the student cannot yet proceed to apply 



540 



ASTRONOMY. 



Astronomy, such observations to actual astronomical determi- 
^'— -V-»^ nations. 

§ V. Of sxderal and mean solar days, years, SiC 
99. We have seen that the earth performs its revo- 
lution on its axis with a motion perfectly uniform ; 
and that the interval between the return of any fixed 
star to the same meridian, is what is called a sideral 
day ; observing that by the same meridian is here to 
be understood, the star appearing: at the same meridian 
altitude ; for the circumpolar stars, as we have seen, 
may be observed twice on the same meridian in the 
course of 24 hours, once in their inferior and once in 
their superior passage ; but they are only once at the 
same meridian altitude. This interval, then, is the 
length of the sideral day ; but it remains for us now to 
explain what is to be understood by a mean solar day, 
or that day which is employed in the common con- 
cerns of life. 



1. Of the mean solar day. 
Mean solar 100. It will be seen in the following articles, that 
'^^y- the interval time between the sun's leaving the first 

point of Aries to its return again to the same, which is 
what is denominated a solar year, is performed in 
about 36.5^ solar days ; or the sun will have appeared 
in that interval 36.5 times on the meridian, and will 
besides have performed nearly one-fourth of his 366th 
revolution : hence, if all the solar days were equal, 
that is, if the sun returned to the meridian of an ob- 
server always after the same interval, the increase of 
his right ascension every day, or the additional angle 
which the earth (having performed a complete revo- 
lution) would have to move through to bring the sun 
again upon the meridian of the observer, would be 

360^" . ,. „ 

equal to -——■ = 59' S"-2 : if, therefore, to the side- 

Soof 
ral day we add the time which the earth employs in 
describing 59' S"-2, we shall have the length of the 
mean solar day : that is, the sideral day is to the 
mean solar day as 360° : 360° 59' 8"-2. 
Consequently, if we call the mean solar day 24 hours, 
according to common reckoning of time, we shall 
have 

360° 59' S" : 360° ) : 24h. : 23h. 56m. 4T' 
which is the length of a sideral day in mean solar 
hours ; and by reversing the first two terms of the 
proportion, we shall have the mean solar day expressed 
in sideral hours. 

2. Sideral year. 
Sideral 101. It appears from what is stated above, and we 

year. have before made the same remark in a general way, 

that the sun has a continual motion in the heavens 
from east to west ; and that after a certain period, he 
will again obtain with respect to the same star, the 
same relative situation ; so that if he were in conjunc- 
tion with it in the first instance, he will return again 
to conjunction after this interval, which is therefore 
called a sideral year. 
Determined In order to determine the duration of this period 
by observa- from observation, take on any day the difference be- 
tion, tween the sun's right ascension and that of the star, 

and when the sun returns to the same part of the hea- 
vens the next year, compare its right ascension with 
that of the same star for two days, one when their 



difference of right ascension is less, and the other when Plane 

greater than the difference before observed ; then it Astronomy, 
will be obvious that at some instant between these ^— "v™^ 
two observations, the right ascension will be exactly 
the same as it was when first observed. 

Now in order to find the precise instant when this 
happens, let us suppose D to be the difference in right 
ascension as observed on the two consecutive days j 
and at the difference between the differences of the 
sun's and stars' right ascension on the first of these 
two days, and on the day when the observation was 
made the day before ; and t be the exact time between 
the intervals of the two transits of the sun over the 
meridian on the two days ; then assuming the motion 
of the sun to be equal in right ascension during this 
interval, we shall have 

^■..-.■...'^ 

the time from the passage of the sun over the meridian 
on the first day, to the instant when it had the same 
right ascension, compared with the star, which it had 
the year before ; and the inter\'al between these two 
times when the difference of right ascension was the 
same, is the length of the sideral year. 

Or if instead of supposing the second observation to 
have been repeated on the second year, there is an 
interval of several years between the two observations, 
and the observed interval of time be divided by the 
number of years, the length of the year will be had 
more exactly, any error in the observations being thus 
rendered less important by being divided into the 
great number of parts. The best time for these obser- 
vations is, when the sun is in or near one of the equi- 
noxes or one of the solstices, his motion in right 
ascension being then exactly or very nearly uniform. 

As an example of this kind, we may state the fol- 
lowing : — 

102. April 1, 1669, at Oh. 3m. 47s. of mean solar gy mm. Pi. 
time, M. Picard observed the difference between the card and 
longitude of the sun and the star Procyon to be 3s. 8° LaCaille. 
59' 36". And M. La CaiUe found the difference of 
longitude between the sun and star to be the same, on 

April 2, 1745, at llh. 10' 45". The sun, therefore, 
made 76 complete revolutions Avith regard to the same 
fixed star in 76 years 1 day llh. 6m. 5Ss. ; or in 
27,759 days llh. 6m. bSs. ; we have, therefore, by 
dividing this interval by 76, 365 days 6h 8' 47" for 
the length of the sideral year ; more recent observa- 
tions, however, give 365 days 6h. 9m. ll'5s. for this 
interval. 

3. Of the tropical year. 

103. The length of the tropical year is the interval The length 
between the sun leaving either equinoctial point to its of the tio- 
return again to the same ; which it does in a less time P'<^^ J'^*''- 
than it passeS^from any fixed star to the same again, 

the latter we have seen is what is termed the sideral 
year ; and the former being that on which the change 
of seasons depend is called the solar or tropical year. 
To determine the length of this year, we may proceed 
as follows : 

Observe the meridian altitude of the sun on the day Determined 
nearest the equinox, and the next year take its meri- fromobser-; 
dian altitude again on two successive days, on the ^*'»°n' 
one when its altitude is greater, and on the other 
when it is less, than in the first observation } then it 



ASTRONOMY. 



541 



A*tronomy. js obvious, that at some intermediate time between 
^"*~V~~^ the two last observations, the sun must have had the 
same tdtitude or declination as in the first instance. 
Now, to find the precise instant, let D be the differ- 
ence of altitude in the two last observations, t the in- 
terval between them, which may be here taken as 24 
hours ; also d the difference between the altitude as 
observed on the first of tlie two latter days, and that 
taken the year before ; tlien, assuming- the declination 
to be uniform, as it actually is at this time, say, as 

2-t d 
T> ', d '.', 24 hours I the time from the first of 

the two latter observations, to the instant when the 
declination was the same as in the preceding year. 
This time, therefore, being added to the niiuiber of 
days between tlie two first observations, will give the 
true length of the solar year. 

Here again, as in last case, if the two observations 
be repeated after an interval of several jears, we may 
look for a result more nearly approximating to the 
truth. 

104. The two following observations v?ere made by 
Cassini and his son, after an interval of 44 years. 

March 20, 1672, Meridian alt. sun's 
upper limb 41° 

March 20, 1722 ditto 41° 

March 21 ditto 41° 

41 51 41 43 O 

41 27 10 41 27 10 



By tljc Cas 
finis. 



43' 0" 
27' 10" 
51' 0'' 



23 50 : J5 50 :: 24 : 15h. 56m. 39s. 

Whence on the 20th of March, at 15h. 56m. 39s., the 
sun's declination was the same as on the 20th of 
March, 1672, at noon. 

Now the interval between the two first of these ob- 
servations was 44 years, 34 of these were common 
years of 365 days each, and 10 of 366 days each, 
making in all an interval of 16,070 days, and therefore 
the interval between the two periods when the sun's 
declination w'as the same was, 16,070 days 15h. 56m. 
39s. and this interval embraces 44 tropical years, 
16,070d. 15h. 56m. 39s. 



whence 



44 



365d. 5h.49'0"53' 



the length of the tropical year, as determined from 
these results ; more recent observations give for the 
tnie length of the tropical vear, 365 days 5 hours 
48' 48". 

4. Precession of the equinoxes. 

Precession 105. It appears from what is stated above, that the 
of the equi- gy^ returns to the equinoxes every year, before it re- 
noxes. turns again to the same fixed star, or to the same 

point in the heavens; the equinoctial points must, 
therefore, have a retrograde motion with respect to 
that of the earth, the cause of which it is not for us at 
present to explain ; we shall, however, hereafter, see 
that it is due to a regular mechanical effect, viz. the 
attraction of the sun and moon upon the earth in con- 
sequence of its spheroidal figure. The effect of this 
is, that the longitude of the stars, which are ahvays 
estimated from the intersection of tlie equator and ec- 
liptic, or from the equinoctial point, or first point of 
Aries, must constantly increase, and by comparing the 
longitude of the same stars at dififerent times^ the mean 
VOL. HI. 



motion of the equinoctial points, or the precession of piane 
thc ecjuinoxes may be determined. Astronomy. 

^Ve have observations of tliis kind from the time of ^>— — ^,-».^ 
Timocharis and Hipparchus ; but we may be allowed 
to entertain considerable doubt as to accuracy ; it will 
be sufficient to observe, that from a comi)arison of the 
best observation, the secular precession, or tliat which 
takes place in 100 years, amounts to 1° 23' 45" or to 
5034" annually. 

5. Anomalistic year. 

106. At a certain time of the year, the sun's dia- Anomalis- 
meter, if measured instrumentally, would be found to t'c year, 
be tlie least ; at which time it is obvious he would be 

the most distant from the earth or in his apogee, that 
is, the earth will then be at one extremity of the trans- 
verse axis of its orbit, and at that extremity which is 
furthest from the sun. Now, if at the end of a cer- 
tain interval, a year from tlie first observation, a 
second were made, and the sun were found in pre- 
cisely the same relative situation with regard to 
certain fixed stars, when his diameter was least, then 
it would be obvious that the sun had always the least 
apparent diameter after the completion of a sideral 
year ; but the astronomical fact is not so ; the sun 
does not return to a point in the heavens where his 
diameter is least in a sideral year; but in an interval 
a little exceeding it, and this interval is what astro- 
nomers have called the anomalistic ijear, the apogee 
has therefore a progressive motion, as we have seen 
the equinoxes have a precession ; the quantity of the 
former, like that of the latter, being found from obser- 
vation. According to the most recent determination, 
the increase in longitude of the sun's apogee in lOO 
years, is 1° 42' 28", or 1' 2-2" annually ; but since 
the precession, which is a regressive motion, is 5034" 
annually, the annual sideral progression is 62-2" — 
5034" = 11'86". Now, the time of describing 
11-86" added to the length of the sideral year, will 
compose an anomalistic year ; and since the sun near 
its apogee moves in longitude about 58' in 24 hours ; 
tlie time will be about 4m. 50s. ; hence the length of 
the anomalistic year,, is equal to 
365d. 6h. 9m. ll-4s. -h 4m. 50s. = 365d. 6h. 14m.l-4s, 

6. Ohliquity of the ecliptic. 

107. The angle contained between the plane of the Obliquity- 
equator and the ecliptic is what is denominated the of the eclip- 
obliquity of the ecliptic ; which is shown from re- ^ic 
peated observations to be variable, like the other 
quantities we have been just examining. We have 
already, in the preceding section, indicated the method 

of determining the measure of this angle by means of 
the greatest and least meridian altitudes of the sun ; 
it will therefore be sufficient in this place to show the 
result of a long succession of such observations by 
different astronomers, which are as follows : — 

o / // 

Eratosthenes, 230 years b.c 23 51 20 Determined 

Hipparchus, 140 years b.c 23 51 20 by different 

Ptolemy, a.d. 140 23 51 10 astrono- 

Pappus, A.D. 390 23 30 ™"'- 

Albatenius, in 880 23 35 40 

Arzachel, in 1070 23 34 O 

Prophatius, in 1300 23 32 O 

Regiomontanus, in 1460 23 30 O 

4a 



J 



542 



ASTRONOMY. 



Astronomy. a i n 

^ ", Waltherus, in 1490 23 29 47 

^^^^ Copernicus, in 1500 23 28 24 

Tyclw, in 1587 23 29 30 

Cassini (the father), in 1656 23 29 2 

Cassini (the son), in 1672 23 28 54 

Flamstead, in 1690 23 28 48 

De la Caille, in 1750 '23 28 19 

Dr. Bradley, in 1/50 23 28 18 

Mayer, in 1750 23 28 18 

Dr. Maslielyne, in 1769 - 23 28 8,5 

M. de Lalande, in 1768 23 28 O 

M. Pond, Ast. Roy. 1816 23 27 50 

Tlie observations of Albatenius, an Arabian, are 
here corrected for refraction. Those of Waltherus, 
M. De la Caille computed. The obliquity by Tycho 
is put down as correctly computed from his observa- 
tions ; also the obliquity, as determined by Flamstead, 
is corrected for the nutation of the earth's axis ; these 
corrections M. de Lalande applied. It is manifest 
from the above observations, that the obliquity of the 
ecliptic continually decreases ; and the irregularity 
which here appears in the diminution, we may ascribe 
to the inaccuracy of the ancient observations, as we 
know that they are subject to greater errors than the 
irregularity of this variation. If we compare the first 
and last observations, they give a diminution of 70'' in 
100 years. If we compare the observation of Lalande 
with that of Tycho, it gives 45". The same com- 
pared with that of Flamstead gives 50''. If we com- 
pare that of Dr. Maskelyne with Dr. Bradley's and 
Mayer's, it gives 50". The comparisons of Dr. Mas- 
kelyne's determination, with that of M. de Lalande, 
which he took as the mean of several results, gives 
50", as determined from the most accurate observa- 
tions. This result agrees very well with that deduced 
from theory ; but the observation of Mr. Pond, as 
compared with those of Bradley, gives QQ" for the va- 
riation in the obliquity in 100 years, or 0-40'' annually. 

§ VI. Oj the corrections for refraction, parallax, SiC. 

1. Of refraction. 

Refraction. 108. ^^Tien a ray of light passes out of a vacuum 
into any medium, or out of a medium into any other 
of a greater density, it is found to deviate from its 
regular coiu-se, towards a perpendicular to the surface 
of the medium into which it enters. (See Optics, p. 427) 
Hence light passing out of a vacuum into the atmo- 
sphere, will, where it enters, be bent or deflected to- 
wards a radius drawn to the earth's centre, the extreme 
surface of the atmosphere being supposed spherical 
and concentric with the centre of the earth ; and as in 
approaching the earth's surface the density of the at- 
mosphere continually increases, the rays of lig'ht are 
constantly entering into a denser medium, and there- 
fore the course of the rays will continually deviate 
from a right line, and describe a curve ; whence, at 
the surface of the earth, the rays of light enter the 
eye of a spectator, in a different direction from that in 
which they would have entered it, if there had been 
no atmosphere. Consequently, the apparent place of a 
body from which the light comes must be different 

Fig. 35. from the true place, as shown in fig. 35. 

Observed 109. Altliough we here State the fact of the refrac- 

by the an- tion of the atmosphere as a necessary consequence of 

cients. 



established laws in Optics, it must not be understood piane 
to have been introduced into astronomy as such ; for Astronomy^ 
it was observed by the ancients long before they ^^-— y-^w^ 
were able to trace its cause to optical principles. 
Nothing is indeed more easy to be detected in astro- 
nomical observation ; for by taking the greatest and 
least altitudes of the circumpolar stars, it will be seen 
that their apparent north polar distances Avill be dif- 
ferent accordingly as it is taken at the time of their 
superior or inferior passage; and this variation is 
observed to be very nearly constant for the same place 
and the same star, and for all stars that have the 
same declination ; but to vary according to a certain 
law, in stars that pass at different altitudes ; it is also 
determinable from observation, that refraction does 
not alter the azimuth of bodies, and the same 
may also be demonstrated on physical principles, 
as we have shown in our treatise on Optics. Re- 
fraction, therefore, has a tendency only to increase 
the apparent altitude of a heavenly body, its entire 
e&'ect being produced in a vertical circle, and its effect 
is less and less from the horizon to the zenith, where 
it vanishes. 

Both Ptolemy and Alhazen were acquainted with Tycbo en- 
this irregularity, and attributed it to its true cause, deavoured 
but neither of them undertook to determine the quan- 1-° estimate 
tity of it. Tycho perceiving that the altitude of the ''» quantity, 
equator, as deduced from the two solstices, was not 
the exact complement of the height of the pole, en- 
deavoured to determine the quantity of refraction due 
to each zenith distance ; he made the horizontal re- 
fraction 34", and supposed it to become insensible at 
45° of altitude ; in the former, he was not far from 
the truth, but the latter conclusion was wholly erro- 
neous ; it is, in fact, to Dominic Cassini that we are 
indebted for the first regular hypothesis on the sub- 
ject of astronomical refraction ; but as his solution 
leads to an expression in which the refraction is made 
proportional to the tangent of the zenith distance, 
diminished by a quantity which itself depends upon 
the refraction sought ; we shall not insist upon it in 
this place, but proceed to illustrate the formulae given 
by Bradley. 

Bradley's formulce. 

110. Various tables of refraction more or less cor- Bradley's 
rect had been already formed, Avhen the above cele- formulas, 
brated astronomer commenced his observations for 
the purpose of deducing more exact formulae than 
were at that time in existence, and of these tables he 
availed himself in settling the law of this important 
astronomical correction. 

By means of numerous observations on Polaris and 
other circumpolar stars, Bradley deduced the apparent 
zenith distance P of the pole. By observations also 
on the sun at the equinoxes, when this body had the 
same zenith distance but opposite right ascensions, 
he deduced the height of the equator. In this in- 
stance, as in the former, it was only the apparent alti- 
tude that was obtained on account of the refraction, 
and therefore greater than the true height, and con- 
sequently, the apparent zenith distance was less than 
the true ; whence the sum of the two zenith distances 
of the poles and the equator (which if true ought to 
be = 90^) will be less than 90°, by the sum of the two 
refractions due respectively to the zenith distances 



ASTRONOMY. 



543 



Astronomy. P and Q. Conceive, for instance, the two refractions 
^— — V"*^ to be p and q, then, 

P + Q = 90° - (p + (?) 
and p + q = 90° — (P + Q) 

consequently, the sum of the two refractions p -\- q'ls 
given, but the object is to determine tliem separately ; 
but, by referring to the best tables extant on this sub- 
ject, it was found, that the diiference q — p was about 
equal to 2 seconds, and lience tlie two equations 
p + g = 90° - (P + Q) 
p — q = <2," 
gave 

9 = 45° 0' \" _ 1 (P + Q) 
p = 44° 59' 59" - I (P + Q) 
Now, according to Bradley's observation, he found 
P = 38° 30' 35'' 
Q = 51° 37' 28" 
whence, p = 57''- 5 and q = 59"' 5 
but this being only an approximation, in order to ob- 
tain a more correct result ; the author separated the 
sum p + q = I' 57" into two parts p' + q' which 
should be to one another as the tangents of the ob- 
served zenith distances ; whence he obtained 

, _ ta n 38° 31' 32"-5 

P — iP + 9) X tan 38° 31' 32"- 5 + tan 51°28'27§" 
tan 51° 28' 271" 



(p' +q) X 



tan 38° 31' 32i" + tan 51° 28' 27|'' 
and by means of the new operation, he foimd 
/ = 4 5"- 5 at the co- altitude 38° 31' 20^" 
q' = 1' ll"-5 ditto 51° 28' 39|" 

111. We have stated above that Bradley assumed 
the refraction to vary as the tangent of the zenith 
distance ; the principle on which this assumption is 
founded, may be illustrated as follows : — 
Fig. 3G. Let CAn, fig. 36. be the angle of incidence, CAm 

the angle of refraction ; and, consequently, niAn the 
quantity of refraction ; let CT be the tangent of the 
arc Cm, mr its sine, nw the sine of Cm, and draw rm 
parallel to vw ; then as the refraction of the arc is 
very small, we may consider mr7i as a rectilinear tri- 
angle ; and hence by similar triangles. 

Am X rn 

n '. m n 



Aw • A i 



A V 



but A m is constant, and as the ratio of m v to m w is 
also constant by the laws of refraction ; their difFer- 

ence r n must vary as m v ,- hence m n varies as -— ; but 

Av 
Am X 771V . mu . 

CI =: : which vanes as --— because Am is 

Av Av 

constant : consequently, the refraction mn varies as 
CT, the tangent of the apparent zenith distance of the 
star; for the angle of refraction CAni, is the angle 
between the refracted ray and the perpendicular to the 
surface of the medium, which perpendicular is directed 
to the zenith ; therefore, while the refraction is very 
small, so that rm7i may be considered as rectilinear, 
this rule may be considered as furnishing a good ap- 
proximation. 
Formation 112. Assuming, therefore, the preceding quantities 
of tables. (^rt. 110) as tlie true or actual refractions, at the alti- 
tude of the pole and equator ; and adopting the above 
analogy with reference to the tangents of the zenith 
distances, Bradley deduced the refractions for other 
altitudes exceeding that of the equator, and for less 



ones or greater zenith distances, he employed the Plane 
circumpolar stars. That is, supposing xt/, (fig. 37) Astronomy. 
to be the true places of a circumpolar star at its least ^~7"^v^'"*' 
and greatest altitude, then Z r, by correcting the ob- ^^°' ^^' 
served distance is known, consequently ZP is known, 
and Px is so likewise. Again, the apparent zenith 
distance of the star at ij, is observed, and subtracting 
from it ZP, the apparent distance from P is knoAvn, 
which is less than the true distance Pij, by a certain 
quantity which is determinable because Pa- = Py, and 
the former has been determined, and this difference is 
obviously the correction due to the zenith distance Zy. 

As an example, it was found by observation on 
Cassiopea at its greatest altitude, that tlie apparent 
zenith distance was 

13° 48' 121" 

Correct for refraction 14 



True zenith dist. 
Zenith dist. of pole 

North polar dist. 



13 48 26| 
38 31 20i 



24 42 54 



Again, by observation, the star being at its least 
altitude above the horizon, the zenith distance was 
found to be 

63° 13' 21"-8 

Subtract 38 31 20'5 



App. N. P. dist. 
True ditto 

Refraction at 63° 
21"-8 Z. D. 



24 42 1'3 

24 42 54 



}« 



52-7 



By means of similar observations, Bradley deter- 
mined the refractions for other altitudes ; and after 
tabulating the results and a due examination of them, 
he found that the law of the refraction instead of 
being simply proportional to the tangent of the zenith 
distance, was of the form 

r — — tan (z — 3 r) 

71 

And deducing from observation the values of m and re 
under different temperatures and different barometri- 
cal pressures, he obtained the formula 

a 400 

refi-c. = ^^ X tan (Z - 3 r) x 57" x ^^^-^-^ 

In which a is the altitude of the barometer in inches 

Z the zenith distance, 

r = 57" X tan Z, 

p = height of Fahrenheit's thermometer, 

29'6 =: mean height of barometer. 
113. This formula is found to apply with consider- Groom- 
able accuracy for all altitudes greater than 10°, but bridge's 
for less altitudes it is very erroneous ; and different fornix!*' 
formulas and tables have accordingly been computed 
by more recent astronomers which approach nearer 
to the truth : of these tlie results published by Mr. 
Groombridge in the Phil. Tran. for 1814, are perhaps 
the most valuable ; his formula, under the medium 
temperature and pressure, is as follows : 

refrac. = tan (z — 3-6342956 r) x 58"- 132967 
which answers for all altitudes above 3° ,- for less al- 
titudes a farther correction becomes necessary ; viz, 
4 a2 



)44 



ASTRONOMY. 



Astronomy, forevery minute below3°of altitude j or for every minute 
>— >^,— »-^ more than 87° of zenith distance, the result found as 
above must be reduced -00462. By means of these for- 
mulae, Mr. Groombridge has computed a very extensive 
table of refractions, with the requisite tables of cor- 
rections for the different states of barometrical pres- 
sure, as well as for thermometrical temperatures, both 
for the outside and inside of the observatory. We 
cannot allow ourselves to transcribe this table in the 



extended form given to it by its author, but the fol- Plane 
lowing abridgment of it will, it is presumed, be found Astronomy, 
highly acceptable to our readers. It will be under- ^"^"V"^ 
stood that the correction for the barometer and ther- 
mometer will be the sum of the two factors in Table 
II. and Table III. multiplied into the mean refraction, 
and the product added or subtracted therefrom, ac- 
cording as the sum of the factors is plus or minus. 



Table of mean refractions, computed from the preceding formula. 



Zen. Dist. 


Refi-ac. 


Zen. Dist. 


Refrac. 


Zen. Dist. 


Refrac. 


Zen. Dist. 


Refrac. 


Zen. Dist. 


Refrac. 


/ 


/ 


^^ 


/ 


/ // 


/ 


/ // 


/ 


/ // 


/ 


/ // 








000 


22° 


23-46 


44 


56-03 


6Q 


2 9-77 


87 8 


14 46-37 


30 





051 


22 30 


24-05 


44 30 


5701 


66 30 


2 12-85 


87 16 


15 14-40 


1 





101 


23 


24-65 


45 


58-01 


67 


2 16-05 


87 24 


15 44-00 


1 30 





1'52 


23 30 


25-25 


45 30 


59-03 


67 30 


2 19-38 


87 32 


16 15-27 


'i 





2-03 


24 


25-85 


46 


1 0-07 


68 


2 22-85 


87 40 


16 48-35 


2 30 





2-53 


24 30 


26-46 


46 30 


1 1-13 


68 30 


2 26-47 


87 48 


17 23-37 


3 





304 


25 


2707 


47 


1 2-20 


69 


2 30-25 


87 56 


18 0-46 


3 30 





3-55 


25 30 


27-69 


47 30 


1 3-30 


69 30 


2 34-21 


88 


18 19-83 


4 





406 


26 


28-32 


48 


1 4-41 


70 


2 38-34 


88 6 


18 49-98 


4 30 





4-57 


26 30 


28-95 


48 30 


1 5-55 


70 30 


2 42-68 


88 12 


19 21-51 


5 





508 


27 


29-58 


49 


1 6-72 


71 


2 47-23 


88 18 


19 54-47 


5 30 





5-59 


27 30 


29-80 


49 30 


1 790 


71 30 


2 52-01 


88 24 


20 28-89 


6 





610 


28 


30-87 


50 


1 911 


72 


2 57-03 


88 30 


21 5-08 


6 30 





6-62 


28 30 


31-52 


50 30 


1 1034 


72 30 


3 2-33 


88 36 


21 42-88 


7 





713 


29 


3218 


51 


1 11-60 


73 


3 7-92 


88 42 


22 22-47 


7 30 





7-64 


29 30 


32-85 


51 30 


1 12-89 


73 30 


3 13-82 


88 48 


23 3-95 


8 





8-16 


30 


33-52 


52 


1 14-21 


74 


3 20-07 


88 54 


23 47-40 


8 30 





8-68 


30 30 


34-20 


52 30 


1 15-55 


74 30 


3 26-69 


89 


24 32-94 


9 





9-20 


31 


34-88 


53 


1 16-93 


75 


3 33-73 


89- 4 


25 4-51 


9 30 





9-72 


31 30 


35-57 


53 30 


1 18-33 


75 30 


3 41-22 


89 8 


25 37-09 


10 





10-24 


32 


36-27 


54 


1 19-78 


76 


3 4921 


89 12 


26 10-71 


10 30 





10-76 


32 30 


36-98 


54 30 


1 21-25 


76 30 


3 57-75 


89 16 


26 45-40 


11 





11-29 


33 


37-70 


55 


1 22-77 


77 


4 6-89 


89 20 


27 21-20 


11 30 





11-81 


33 30 


38-42 


55 30 


1 24-31 


77 30 


4 16 72 


89 24 


27 58-14 


12 





12-34 


34 


39-15 


56 


1 25-91 


78 


4 27-30 


89 28 


28 36 26 


12 30 





12-87 


34 30 


39-89 


56 30 


1 2754 


78 30 


4 37-72 


89 32 


29 15-60 


13 





13-40 


35 


40-64 


57 


1 29-21 


79 


4 51-09 


89 36 


29 56-19 


13 30 





13-94 


35 30 


41-40 


57 30 


1 3093 


79 30 


5 4-53 


89 40 


30 38-07 


14 





14-48 


36 


42-17 


58 


1 32-69 


80 


5 19-18 


89 44 


31 21-28 


14 30 





15-02 


36 30 


4295 


58 30 


1 34-51 


80 30 


5 35-21 


89 48 


32 5-85 


15 





15-56 


37 


43-74 


59 


1 36-38 


81 


5 52-83 


89 52 


32 51-82 


15 30 





16-10 


37 30 


44-53 


59 30 


1 38-30 


81 30 


6 12-26 


89 56 


33 39-84 


16 





1665 


38 


45-34 


60 


1 40-28 


82 


6 33-79 


90 


34 28- 13 


16 30 





17-20 


38 30 


46-16 


60 30 


1 42-32 


82 30 


6 57-78 


90 2 


34 5315 


17 





1775 


39 


4700 


61 


1 44-42 


83 


7 24-63 


90 4 


35 18-55 


17 30 





18-31 


39 30 


47-84 


61 30 


1 46-59 


83 30 


7 54-87 


90 6 


35 44-34 


18 





18-86 


40 


48-69 


62 


1 48-83 


84 


8 29- 13 


90 8 


36 10-52 


18 30 





19-43 


40 30 


49-56 


62 30 


1 51-14 


84 30 


9 8-18 


90 10 


36 37-10 


19 





19-99 


41 


50-44 


63 


1 53-53 


85 


9 53-03 


90 12 


37 4-OS 


19 30 





20-56 


41 30 


51-34 


63 30 


1 56-00 


85 30 


10 44-88 


90 14 


37 31-47 


20 





21-13 


42 


52-25 


64 


1 58-56 


86 


11 45-57 


90 16 


37 59-28 


20 30 





21-71 


42 30 


53-17 


64 30 


2 1-21 


86 24 


12 41-02 


90 18 


38 27-50 


21 


22-29 


43 


54-11 


65 


2 3-96 


■ 87 48 


13 44-62 






21 30 





22-87 


43 30 


55-06 


65 30 


2 6-81 


1 87 


14 19-80 







ASTRONOMY. 



645 



Correction to preceding table of refraction. 



Astronomy. 























Plane 




BAROMETER. 






FAHRENHEIT'S THERMOlMETER. 




Astronomy 


Inches. 


Correc. 


luches. 


Correc. 

+ 


Degree. 


Within. 

+ 


Witliout. 

+ 


Degree. 


Within. 


Without. 




28-60 


•0350 


29-60 


•0000 


24-0 


•0575 


■0420 


490 


-0000 


-oo&o 




62 


•0342 


62 


•0007 


24-5 


•0563 


■0410 


49-5 


-0011 


-0090 




64 


•0335 


64 


•0014 


25-0 


-0552 


■0400 


500 


•0022 


-0100 




66 


•0328 


66 


•0020 


25-5 


•0540 


•0390 


50-5 


•0033 


-0110 




63 


■0321 


68 


•0027 


26-0 


•0529 


•0380 


510 


•0044 


-0120 




28-70 


-0314 


29-70 


•0034 


26-5 - 


-0517 


•0370 


51-5 


•0055 


-0130 




72 


•0306 


72 


•0041 


27-0 


-0506 


•0360 


52-0 


•0066 


-0140 




74 


•0299 


74 


•0047 


27-5 


•0494 


•0350 


52-5 


•0077 


■01.50 




76 


•0292 


76 


•0054 


28^0 


•0483 


•0340 


53-0 


•0088 


-0160 




78 


-0285 


78 


•0061 


28-5 


•0471 


•0330 


53-5 


•0099 


-0170 




28-80 


•0278 


29-80 


•0068 


29-0 


•0460 


•0320 


540 


•0110 


-0180 




82 


•0271 


82 


•0074 


29-5 


•0448 


■0310 


54-5 


•0121 


-0190 




84 


•0264 


84 


•0081 


30-0 


•0437 


■0300 


550 


•0132 


-0200 




86 


•0256 


86 


•0088 


30-5 


•0425 


■0290 


55-5 


•0143 


-0210 




88 


•0249 


88 


•0095 


31-0 


•0414 


■0280 


560 


-01.54 


•0220 




28-90 


•0242 


29-90 


•0101 


31-5 


•0402 


•0270 


56-5 


•0165 


-0230 




92 


-0235 


92 


-0108 


32-0 


•0391 


•0260 


570 


•0176 


-0240 




94 


•0228 


94 


•0115 


32-5 


•0379 


•0250 


575 


-0167 


•0250 




96 


•0221 


96 


•0122 


33-0 


•0368 


•0240 


58-0 


-0198 


-0260 




98 


•0214 


98 


•0128 1 


33-5 


•0356 


•0230 


58-5 


•0209 


-0270 




2900 


•0207 


30-0O 


•0135 1 


34-0 


•0345 


•0220 


590 


•0220 


•0280 




02 


•0200 


02 


•0142 i 


34-5 


•0333 


•0210 


59-5 


-0231 


•0290 




04 


•0193 


04 


•0149 


350 


•0322 


•0200 


600 


•0242 


•0300 




06 


•0186 


06 


•0155 I 


355 


•0310 


•0190 


60-5 


■0253 


•0310 




OS 


•0179 


08 


•0162 j 


360 


•0299 


•0180 


610 


■0264 


•0320 




29-10 


■0172 


3010 


•0169 1 


36-5 


•0287 


•0170 


61-5 


■0275 


-0330 




12 


•0165 


12 


•0176 


370 


•0276 


•0160 


620 


■02S6 


-0340 




14 


•0158 


14 


•0182 


37-5 


•0264 


•0150 


62-5 


■0297 


-0350 




16 


•0151 


16 


•0189 


38-0 


•0253 


•0140 


630 


■0308 


-0360 




18 


•0144 


18 


•0196 


38-5 


•0241 


•0130 


63-5 


■0319 


-0370 




29-20 


•0137 


30-20 


•0203 


390 


•0230 


•0120 


640 


■0330 


-0380 




22 


-0130 


22 


•0210 


39-5 


•0218 


•0110 


64-5 


■0341 


-0390 




24 


•0123 


24 


•0216 


40-0 


•0207 


•0100 


650 


■0352 


-0400 




26 


•0116 


26 


•0223 


40-5 


•0195 


•0090 


65-5 


■0363 


-0410 




28 


•0109 


28 


•0230 


41-0 


■0184 


•0080 


66-0 


■0374 


-0420 




29-30 


•0102 


3030 


•0237 


41-5 


•0172 


•0070 


66-5 


■0385 


-0430 




32 


•0096 


32 


•0243 


42-0 


•0161 


•0060 


67-0 


■0396 


-0440 




34 


•0089 


34 


•0250 


42-5 


•0149 


■0050 


67-5 


■0407 


-0450 




36 


•00&2 


36 


•0257 


43-0 


■0138 


•0040 


68-0 


■0418 


-0460 




38 


•0075 


38 


•0264 


43-5 


■0126 


•0030 


66-5 


•0429 


-0470 




29-40 


•0068 


30^40 


•0270 


44-0 


■0115 


•0020 


690 


■0440 


•0480 




42 


•0061 


42 


•0277 


44-5 


■0103 


•0010 


69-5 


■0451 


•0490 




44 


•0054 


44 


-0284 


45-0 


■0092 


— 


700 


•0462 


•0500 




46 


•0048 


46 


•0291 


45-5 


■0080 


•0010 


70 5 


•0473 


•0510 




48 


•0041 


48 


•0297 


460 


■0069 


•0020 


710 


-0484 


-0520 




29-50 


•0034 


30-50 


•0304 


46-5 


-0057 


•0030 


71-5 


-0495 


-0530 




52 


•0027 


52 


•0311 


47-0 


-0046 


•0040 


720 


•0506 


-0540 




54 


•0020 


54 


•0318 


47-5 


•0034 


•0050 


72-5 


•0517 


-0550 




56 


•0014 


56 


•0324 


480 


-0023 


■0060 


730 


•0528 


-0560 




58 


•0007 


58 


-0331 


48-5 


-001 1 


■0070 


73-5 


-0539 


-0570 





546 



ASTRONOMY. 



Astronomy. H^. What we have hitherto stated^ relates princi- 
pally to corrections requisite to be made in astrono- 
mical observations in consequence of the effect of 
refraction in elevating all the heavenly bodies, but the 
same principles will also explain some other astrono- 
mical phenomena, as for instance, the morning and 
evening twilight, the oval appearance of the sun in 
the horizon, the horizontal moon, &c. 
Cause of 115. With respect to the twilight, it arises both 

the twilight from the refraction and reflection of the sun's rays by 
the atmosphere. It is probable, that the reflection 
arises principally from the exhalations of different 
kinds with which the lower beds of the atmosphere are 
charged ; for the twilight lasts till the sun is farther 
below the horizon in the evening than it is in the 
morning when it begins, and it is longer in summer 
than in winter. Now in the former case, the heat of 
the day has raised the vapours and exhalations ; and 
in the latter, they will be more elevated from the heat 
of the season ; therefore, supposing the reflection to 
be made by them, {he twilight ought to be longer in 
the evening than in the morning, and longer in the 
summer than in the winter. 

Commonly, it is' assumed, that the twilight begins 
when the sun is 18° below tlie horizon ; but in our 
investigations relative to the time of shortest twilight 
(art. 78), we have left the solution general for any 
number of degrees, and which may therefore be sup- 
plied at pleasure. 
Oval figure 116. Another effect of refraction, as we have above 
of the sun observed, is that of giving the sun and moon an oval 
?'*'' ™°°'^. appearance in consequence of the refraction of the 
zon ^ °"' lower limb being greater than the upper ; whereby 
the vertical diameter is diminished. For assuming 
the diameter of the sun to be S%', and the lower limb 
to touch the hoi'izon, then the mean refraction at that 
limb is 33' ; but the altitude of the upper limb being 
32', its refraction is only 28' 6", the difference of 
which is 4' 54", the quantity by which the vertical 
diameter appears shorter than that parallel to the ho- 
rizon. Tliis, however, will only happen wlien the 
body is in or very near the horizon, for when the al- 
titude is any considerable qtiantity, the refraction of 
both limbs being then very nearly tlie same, the appa- 
rent disc will not differ sensibly from a circle. 

2. Of parallaxes. 

Paralla . 117- Parallax is a term used by astronomers to 

denote an arc of the heavens intercepted between the 
true and apparent place of a star, or other heavenly 
body, or its place as viewed from the centre and the 
surface of the earth, 
p. 27 Let s (fig. 37) represent a star, C the centre of the 

earth, Z the zenith of a spectator, then the observed 
zenith distance of s is the angle ZA s, but its actual 
zenith distance, as viewed from the centre C, is ZCs, 
and the difference between the angles ZCs and ZAs is 
is A.sC, which is called the angle of parallax. 

Now we know from the principles of trigonometry 
that 

CA CA 

sin CsA = sin CAs x » " = sin ZAs x 

Cs C s 

whence if CA, Cs remain the same, the sine of CsA, 
that is, the sine of the parallax varies as the sine of 
the star's zenith distance. Consequently, the parallax 



must be greater, the greater the zenttli distance 5 It Plane 
must therefore be greatest when the body is seen in Astronomy, 
the horizon, or when the zenith distance is 90°. Let p ^>"»-v-*^ 
represent the parallax at any zenith distance Z, P the 
greatest or horizontal parallax, then we shall have 

C A C 4 PA 

sin p =: — X sin Z, and sin P = •;^ x sin 90° = — 



Cs Cs 

Consequently, sin p = sin P sin Z 
If therefore the parallax be known for any one zenith 
distance, it may be determined for any other; and 
moreover, if CA the earth's radius, and Cs the distance 
of the body, were given, the parallax P would become 
known ) and conversely, if the parallax were given, 
the distance Cs might also be determined, the radius 
of the earth being supposed known from geodetic 
operations. It is, in fact, from knowing the parallax 
of one or more of the heavenly bodies, that their dis- 
tances have been determined. 

The correction for parallax is one of the most im- 
portant in practical astronomy, and accordingly, va- 
rious methods have been proposed by different as- 
tronomers for determining it ; but of these we shall 
only specify one or two of the most obvious. 

118. First, to find the parallax of the moon. Take Parallax of 
the meridian altitudes of the moon when it has its the moon, 
greatest north and south latitudes, and correct them 
for refraction, a,s explained in the preceding chapter. 
Then, if there were no parallax, or if the parallax 
were the same at both altitudes, the difference of the 
altitudes thus corrected would be equal to the sum of 
the latitudes, and consequently, what those quantities 
want of equality will be equal to the difference of the 
parallax. We have, therefore, by means of these 
observations, the difference of the parallaxes at these 
altitudes, and it is required to find them separately. 
For this purpose, let us denote the two zenith dis- 



tances, by Z, z, the parallaxes by P, p 
what has been stated above we have 

sin Z : sin 2 : ; P : 75 
or sin Z — sin' 2 ". sin. 2 \\ P — p 

sin 2 (P-p) 



then from 



whence 



sinZ — sinz 
the parallax at the greatest altitude. 

We here suppose the moon to be at the same dis- 
tance from the earth at both observations j when this 
is not the case, one of tlie observations must be re- 
duced to what it would have been had the distance 
been the same. 

119. Let a body P (fig. 38) be observed from two Determined 
places. A, B, in the same meridian, then the whole hy observa- 
angle APB is the sum of the two parallaxes at those p?°^oo 
two places. Nov/ v/eliave seen in article llf, that the '^' 

Darallax APC or p = P x sin PAL 

parallax PBC or p' = P X sin PBM 
Hence APB = p J- / = P x (sin VKL + sin PBM) 
Consequently 

■hor. parallax (P) = -TpXiT^^-pBM 

In order to illustrate this by actual observation, we 
may state the following example : 

October 5, 1751, M. De la CaiUe, at the Cape of 
Good Hope, observed Mars to be 1' 25"-8 below the 
parallel of X in Aquarius, and at 25° distance from the 
zenith. On the same day, at Stockholm, Mars was 



ASTRONOMY. 



547 



J 



Astronomy, obsei-ved to be 1' S/'^'T below the parallel of the same 
t_ , _ ^y starj and at 68° 14' zenith distance. Hence 

from 1' 57'''7 

take 1 25-8 



angle APB = 
Whence P = 



j3+/=0 31'9 
31-9" 



23-6 



sin 25° + sin 68° 14' 
The horizontal parallax of Mars being thus deter- 
mined, we may hence find that for the sun ; for we 
have seen that^ generally, 
PA 
P= — (see fig. 36) 

Consequently^ since CA, the radius of the earthy is 
constant^ the parallax will vary reciprocally as the 
distance of the body; knowing, therefore,, the pro- 
portional distance of the sun and Mars from the earth 
at the time of observation ; the parallax of the for- 
mer may be determined when that of the latter is 
given. This method, however, of determining the 
solar parallax is not sufficiently accurate for the pur- 
poses of modern astronomy. 

120. Method of determining the parallax in right 
ascension and declination. 
Parallax in Let EQ (fig. 39) be the equator, P its pble, Z the 
zenith, v the true jjlace of the body, and r the appa- 
rent place, as depressed by parallax in the vertical 
circle Z/f, and draw the secondaries Yva, Yrh, then 
at is the parallax in right ascension, and rs in de- 
clination. 

Now vr \vs\\ rad ; sin «rs or Zi)P 

and vs'. ah \\ cos va '. rad 

Hence by multiplication, and rejecting the like factors^ 
vr \ ah '. cos « a '. sin Z t) P 

, vr sin Zz)P 
therefore ao = 



jht ascen- 



declination 
Fig. 39. 



but 
and 



hence 



cos V a 
vr = hor. par, (P) x vZ 
sin r Z : sin ZP : : sin ZPu : sin ZuP 

. ^ ^ sin ZP X sin ZPi> 

smZ»P = 



whence by substitution 

P X sin ZP 



ah = 



sin«Z 



sin ZP« 



cos V a 
Hence it follows, that for the same star, where the 
hor. par. or (P) is given, the parallax in right ascen- 
sion varies as the sine of the hour angle. 
Also, 

ah cos va 

hor. par. = — —-i— „„ 

^ sin ZP X sin ZPu 

In the eastern hemisphere, the appai-ent place b lies 
on the equator to the east of a its true place, and 
therefore the right ascension is diminished by paral- 
lax ; but in the western hemisphere h lies to the 
west of c, and therefore the right ascension is in- 
creased. Hence, if the right ascension be taken before 
and after the meridian, the whole change of parallax 
in right ascension between the two observations, is 
the sum (s) of the two parts before and after the me- 
ridian, we have therefore 

vr 
s ■— ■ X S 



, 7 ,T»s o >-ua uu, riane 

and hor. par. (P).= ^.^^p ^ g ^„o^ 

On the meridian there is no parallax in right ascension. rT'T^'T' 

In order to apply this rule, observe the right ascen- of"i,is^ ^°'^ 
sion of the planet when it passes the meridian, com- method. 
pared with that of a fixed star, at which time there is 
no parallax in right ascension ; about six hours after, 
take the difference of their right ascensions again, 
and observe how much the difference (d) between the 
apparent right ascension of the planet and fixed star 
has changed in that time. Next observe the right 
ascension of the planet for three or four days when it 
passes the meridian in order to get its true motion in 
right ascension. Then if its motion in right ascension 
in the above interval of time, between tlie taking of 
the right ascensions of the fixed star and planet on 
and off tlie meridian, be equal to d, the, planet has no 
parallax in right ascension ,• but if it be not equal to d, 
the difference is the parallax in right ascension, and 
hence, on the above principles, the horizontal parallax 
will be known. Or one observation may be made 
before the planet comes to the meridian and anotlier 
after, by wliich a greater difference v/ill be obtained. 

121. In order to illustrate this method by an ex- By exam- 
ample, let the following be taken : pl^- 

On August 15, 1719, Mars was very near a star of 
the 5th magnitude in the eastern shoulder in Aquarius : 
and at 9h. ISm. in the evening, Mars followed the 
star in 10' 17"; and on the 16th, at 4h. 21m. in the 
morning, it followed it in IC/ 1", therefore in that 
interval, the apparent right ascension of Mars had 
increased 16" in time. 

But according to observations made in the meridian 
for several days after, it appeared that Mars ap- 
proached the star only 14" in that time, from its pro- 
per motion ; therefore 2" in time or 30" in motion was 
the effect of parallax in the interval of the obser- 
vations. 

Now the declination of Mars was 15° 

the co-latitude 41° 10' 

the two hour angles -j o oq/ 

Consequently, the horizontal parallax 
^ 30" X cos 15° 



S denoting the sum of the sines of the two hour angles. 



sin 41° 10' (sin 49° 15' + sin 56° 39') ^ 

At the time of these observations, the distance of tlie 
earth from Mars was to its distance from the sun as 
37 ; 100 ; whence the sun's horizontal parallax is 
found to be 10- 17". 

122. Besides the effect of parallax in right ascension Effect of 
and declination, it is manifest that the latitude and parallax in 
longitude of the moon and planets must also be |atitudeand 
effected by it, and as the determination of this, in " " 
respect to the moon, is, in many cases, particularly 
in solar eclipses, of great importance, we sliall pro- 
ceed to show how it may be computed, supposing the 
latitude of the place, the time, and consequently the 
sun's right ascension, the moon's true latitude and 
longitude, and her horizontal parallax to be given. 

Let HZR (fig. 40) be the meridian, tEQ the equa- pio-. 40. 
tor, p its pole; tC the ecliptic, P its pole; t the 
first point of Aries, HQR the horizon, Z the zenith, 
ZL a secondary to the hoi-izon, passing through the 
true place r, and apparent place t, of the moon ; 
draw P t, Pr, which produce to s, drawing the small 



s^sm 



548 



ASTRONOMY. 



Astronomy, circle ts parallel to ov, and rs is the parallax in lati- 
^—-V*^ tude, and ov the parallax in longitude. Draw the 
great circles r P. PZAB, Pp d e, and ZW perpendicu- 
lar tope; then as tP= 90°, tp= 90°, T must be 
the pole of Pp d e, and therefore cZ t = 90° ; conse- 
quently, d is one of the solstitial points ; viz. either 
s or Yf , draw also 7jx perpendicular to Pr, and 
join Z TT, pT ■ Now tE, or the angle TjoE, or Zp T is 
the right ascension of the mid heaven which is known ; 
PZ = AB, (because A Z the complement to both) 
the altitude of the highest point A of the ecliptic 
above the horizon, called the nonagesimal degree, 
and tA, or the angle ttPA, is its longitude. 

Now in the right angled triangle ZpW, we have 
Zp the co-latitude, and the angle Zp W, the difference 
between the right ascension of the mid heaven t P E 
and Te, to findpW ; hence PW = pW ^ pP, where 
the upper sign is to be taken when the right ascension 
of the mid heaven is less than 180°, and the under 
when greater. 

Again, in the triangle WZ p, WZP, we have 
sin Wp : sin WP :: cot Wp Z : cot WPZ, or tan AP r 
and as we know t o, or tPo, the true longitude of 
the moon, we know APo, or ZPa: : also cos VVPZ^ or 
sin rPZ : rad 1 1 WP : tan ZP. 

Hence in the triangle ZPr, we know ZP, Pr, and 
the angle P, from which the angles ZrP, or trs, and 
Zr may be found ; for in the right angled triangle 
ZPx we know ZP, and the angle P to find Tx, there- 
fore we know rx, and hence, as the sines of the seg- 
ments of the base of any triangle are inversely as the 
tangents of the angles at the base adjacent to which 
they lie, we may find the angle Zrx, with which and 
rx, we may find Zr, the true zenith distance, to 
which, as if it were the apparent zenith distance find 
the parallax by (art. 117) and add it to the true ze- 
nith distance, and we shall have very nearly the ap- 
parent zenith distance, corresponding to which find 
the parallax rt; then in the right angled triangle rsf, 
which may he considered as plane, we know r t and 
the angle r to find rs the parallax in latitude ; find ts, 
which multiplied by the secant of tv, the apparent 
latitude gives the arc ov the parallax in longitude. 

Example. 

Example 123. On January 1, 1771^ at 9 hours apparent time, 

in latitude 53° north, the moon's true longitude was 
3s. 18° 27' 35", and latitude 4° 5' 30'^ S ; also its 
horizontal parallax was 61' 9", to find its parallax in 
latitude and longitude. 

The sun's right ascension was by the tables 282° 
22' 2", and its distance from the meridian 135°, also 
the right ascension tE of tiie mid heaven was 57° 22' 
2", hence the whole operation for the solution of the 
triangles may stand thus : 









Tr 


iangle 


Zp 


W 




ZpW 


_ 


32 37 


1/ 
58 .. 




. cos 


9-9253864 


Zp 


~ 


37 
32 




23 


.. 

57 .. 




. tan 
.tan 


9-887 11 44 


pW 


9-8025008 


Pp 


~ 


23 


28 











PW 


55 


51 


57 





Triangle WpZ Kane' 

pW =32 23 57 AC sin 02709855 Astronom7^ 

PW = 55 51 57 sin 99178865 '""''^r'^ 

ZpW = 32 37 53 cot 101935941 



APT 

oPr 


; 


67 29 
108 27 


8 ., 
35 


rle WPZ 


.tan 

. sin 
10 — 


10-3824661 


oPA 
APZ 


40 58 

67 29 
55 51 


27 

Trians. 

8 . . 

57 .. 


9-9655700 
2016S8210 


WP 


. . tan + : 



ZP 

ZPx 



= 57 56 3G tan 10-2032510 

Triangle ZPa; 

= 57 56 36 , ... tan 102032555 

= 40 58 27 cos 9-8779500 



= 50 19 33 



tan 100812055 



Pr = 94 5 30 

Triangles ZPx, Zrx 

rx = 43 45 57 AC sin 0.1600743 

Px = 50 19 33 sin 9-8863144 

ZPa: = 40 58 27 tan 99387676 



Zra- 
Zr.r 



44 116 tan 99851563 

44 1 16 cos + 10 19-8567795 

43 45 57 tan 9-9812846 



53 6 10 cot 9-8754949 



Z? = 53 6 10 

hor.par. = 6V 9" = 



. . sin 9-9029362 
. . log 3-5645477 



rt, uncorrected 2934" = 48' 54" log 34674839 



App. Z. Dist. Z<53°55'4"nearly sin 99075042 
hor. par 3669" log 35645477 



par. ft corrected=2965"=49' 25" log 3-4720519 



Triangles trs 

par. rt corr. 2965 = 49' 25" log 3-4720519 

^rs = 44° 1' 16" cos 98567795 



•s par. in lat. = 2132" 35' 32" . . log 33288314 



ri corrected = 2965" log 34720519 

trs = 44° 1' 16 sin 98419369 



ts = 2061" = 34' 21" log 3-3139888 

true lat. ro = 4° 5' 30" 

app.lat. tv = ro — rs= 4° 41' 2" sec 100014528 



ov par in long. = 2067" = 34' 27 log 33154416 
The value of i« is equal to ro -1- rs, according as the 
moon has north or south latitude. 

124. The above operation supposes the moon's Remarks^ 
horizontal parallax to have been determined. Ac- 
cording to tlie tables of Mayer, the greatest parallax, 
of the moon, or when she is in her perigee and in op- 
position, is 61' 32"; the least parallax (or when she 



ASTRONOMY. 



549 



Astronomy, is in her apogee nnd in conjunction'^ is 53' 52'' in the 

^— ^Y'-*-^ latitude of Paris : now as the parallax varies inversely 

as the distance, the parallax at the mean distance of 

the moon is 57' 24" viz. an harmonical mean between 

the two former. 

But Delarabre recalculated the parallax from the 
same observations from which Mayer calculated it, 
and found a slight disagreement in the two results. 
He made the equatorial parallax 57' 11"'4 ; Lalande 
made it 57' 5" at the equator, 56' 53"'2 at the pole, 
and 57' 1'^ for the mean radius of the earth ; upon a 
supposition that the ratio of the equatorial and polar 
axes was as 300 ; 299. 

Assuming then the mean parallax to be 57' I", we 
have, referring to fig. 36, 

AC ; mean radius r ',] T>, dist. of moon '. sin 57' l'' 
hence D = 603 rad = 603 x 3964 = 239029 miles 
the mean distance of the moon from the earth. — 
Vinces Astronomy. 

The preceding methods by which the parallaxes of 
the moon and of Mars have been determined are 
not sufficiently exact for us to employ them in deter- 
mining that of the sun. And since this is in astro- 
nomy a most important element, and requires the 
most exact determination, it has, as we have before 
remarked, engaged the most anxious attention of 
philosophers, and no one has rendered in this re- 
spect a more essential service to the science than Dr. 
Maskelyne, our late worthy astronomer royal ; but the 
method which he employed, and which was first 
pointed out by the celebrated astronomer Dr. Halley, 
cannot be with propriety illustrated in this place, be- 
cause it supposes the planetary motions to be deter- 
mined to the utmost accuracy : in a subsequent chap- 
ter we shall, however, enter at some length upon the 
explanation of this method, at present it will be suffi- 
cient to state that it depends upon the transit of either 



and refraction, agreeably to what has been taught in Plane 



the preceding articles 



Observation. 



Astronomy. 



Alt. O upper limb. , 
Lower limb , 



App. alt. O centre 
App. zen. dist. . . . 
+ Refraction 



62 44 11 
62 15 41 



2) 


124 


59 


52 




62 

27 



29 
30 



56 

4 

29 


ax 


27 30 33 
4 




27 
48 


30 29 
50 14 



sin = 4617 



(8"| X -4617) parallax 

Corr. alt. Q's centre. 
Latitude of the place. 

O's declination 21 29 45 

3. Of the correction for aberration. 
126. In our historical chapter, we have given some Aberration, 
account of this important astronomical discovery; 
it remains for us in this place to enter a little more at 
length into an illustration of the principles, and to 
describe the method of computing and applying the 
requisite corrections. 

The situation of any object in the heavens is determin- 
ed by the position of the axis of the telescope, attached 
to the instrument with which we measure ; for such 
a position is given to the telescope, that the rays of 
light from the object may descend down the axis, and 
in that situation, the index shows the angular distance 
required ; if, therefore, the observer were in a state of 
absolute rest, while he was making his observation, 
the direction of his telescope would coincide with that 



cieni 10 state inat 11 aepencis upon me cransii or eiiner „f +>,o ^k,'o«<- „^ -t^ ii i i.i in 

r.u X • r ■ ^ ^ X. / i- i t .t_ ^ r tt- ^'^ t"^ oDjcct, as it would also, althouph he Were in 

of the two inferior planets, but particularly that of Ve- rv,„t;^„ ;f i;^>,f „,„. • t- ^ i ""&" '^^ "*=''^ m 

,, ,_ ,^ _ _ /, .1 _f_.. i.._,_./ ,, P , motion, it light was instantaneously transmitted from 

the luminous body to the eye. But if, as is actuaUy 



mis over the sun's disc ; and that it has been thus found 
to be 8"'75 according to Maskelyne, but S"81 accord- 
ing to Laplace ; Avhereas we have seen (art. 121) that 
as deduced from observations on Mars, it was found to 
be 10"- 17. 

From what has been stated it appears, that the 
parallaxes of the planets answer two important pur- 
poses, for we hence may determine their actual dis- 
tances from the earth, and moreover, without a know- 
ledge of the quantity of this important datum, we 
should be unable to correct our observations, and 
much uncertainty would consequently attend all our 
deductions. The parallax of the sun being very small, 
its mean horizontal parallax may be considered as 
constant, viz. 8"-75, and consequently, the parallax 
for any altitude is readily determined by means of 
the formula 

p = P X sin zen. dist., or 

p = 8"-75 X sin zen. dist. 



the case, the motion of light is progressive, Avhile the 
observer is also carried forward in space, then, except 
in the particular instance in which both motions take 
place in the same line, a different direction must ne- 
cessarily be given to the axis of the telescope ; and 
consequently, the place measured in the heavens will 
be different from the true place. 

127. This may be illustrated in a general manner Illustrated, 
as follows. Lets' (fig. 41) be a fixed star, VF the F> 41 
direction of the earth's motion, S'F the direction of a ° 
particle of light, entering the axis a c of the telescope, 
at a, and moving through a F, while the earth moves 
from c to F ; and if the telescope be kept parallel to 
itself, the light will descend in the axis. For let the 
axis nm,¥w, continue parallel to ac; and if each 
motion be considered as uniform, that of the spectator 
occasioned by the earth's rotation being disregarded 
on account of its being too small to produce any sen- 



But for the moon, the parallax being considerable, we sible effect, the spaces described in the same time 

ought, in delicate observations, to compute it for her will preserve the same proportion; but cF and Fa 

actual distance, and accordingly, in the Nautical Al- being described in the same time, and as we have 

manack, we find the lunar parallax, as well as her cF ; Fa '.'.en : av ' 

semi diameter, stated for 12 o'clock, both at noon and it follows, that era and a V will be described in the 

midnight, for every day in the year. same time ; therefore, when the telescope is in the 

125. Let us now propose an example to show the situation nm, the p»rticle of light will be at v in the 

method of introducing the corrections for parallax telescope 3 and the case being the same at every 

VOI-. III. 4 B 



J 



550 



ASTRONOMY. 



Astronomy. 



Tlie place 
sliown by 
the teles- 
cope the 
same as 
shown to 
the naked 
eye. 



Ratio of 
Tel. of light 
to the vel. 
of earth. 



Compared 
with other 
observa- 
tions. 



moment of its descent, the place measured by the 
telescope at F is s', and the angle S'FV, is the aber- 
ration or the difference between the true place of the 
star and the place measured by the instrument. 
Hence it appears, that if we take 
FS : Fi : : vel. of light : vel. of the earth, 
join St and complete the parallelogram F< Ss, the 
aberration will be equal to FSi ; S will be the true 
place of the star, and s the place measured by the in- 
strument, and this latter is the same with the apparent 
place of the object as it woidd be seen by the naked 
eye. This will appear as follows. 

128. If a ray of light fall upon the eye in motion, 
its relative motion with respect to the e}'e, will be 
the same as if equal motions Avere impressed in the 
same direction upon each, at the instant of contact ; 
for equal motions in the same direction impressedupon 
two bodies Avill not effect their relative motions, and 
therefore the effect one upon the other will not be 
altered. Let then YF be a tangent to the earth's or- 
bit at F, and therefore represent the direction of the 
earth's motion at that instant, and S' a star : join ST 
and produce it to G ; take 

FG : F« :: vel. of light : vel. of the earth, 
and complete the parallelogram FGH« ,- join also 
FH : then since FG, and F« represent the motions of 
light. and of the earth, we shall have on the principle 
of the composition of motion explained (art. 24) 
Mechanics, FH, for the corresponding resulting mo- 
tion ; that is, the object will appear in the direction 
of the diagonal FH, and GFH or its equal S'F/ or 
FS< will be the aberration; consequently, the apparent 
place to the naked eye is the same as that determined 
by the telescope. 

129. Now we have by trigonometry, 

sin FS^ : sin FfS : I Fi : FS : : vel. of earth : 
the vel. of light '. whence 

F* 

sin YSt = sin FiS x r^ 

Fs 

. vel. of earth 

or sm of aberration = sm FfS x — ; — ^ ,. . , 

vel. of light 

therefore considering the ratio of the velocity of light 
and of the earth as constant, the sine of aberration or 
the aberration itself, will vary as the sine of FfS, and 
is therefore greatest when that angle is a right angle, 
and it will be zero when the angle F<S vanishes, that 
is, when the motions of the earth and of light are 
made in the same right line. 

By observations it has been determined, that the 
greatest effect of aberration is 20", and as this corres- 
ponds to the case of FiS = 90°, or sin F<S = l.we have 
vel. of earth 
sin 20'' =1 X , t V ^.^ 
vel. of light 

vel. of earth \ vel. of light as sin 20" '. rad. ; \ 
1 : 10314 

130. This result is obtained frora observation, and 
is independent of any deductions drawn from the ac- 
tual velocity of the. luminous rays ; it only shows 
that if light moved with the velocity indicated, that 
such phenomena ought to have place, and that it may 
therefore be employed as an illustration of them. 
But the actual velocity of light has been otherwise 
determined ; let us see, therefore, how nearly the 
results in the two cases agree with each other. 

For this purpose, call the radius of the earth's orbit 



r, and we shall have 3-1416 x 2 r for the circumfer- 
ence which is described by the earth in 36o\ days, or . 

31557600 seconds ; consequently, vnll 

^ ^' 31557600 
be the velocity per second, and by the above deter- 
mination, 

10314 X 3-1416 X 2r 

= the velocity of light per 



31557600 



second. 
Hence as 



10314 X 3-1416 X 9.1 



31557600 



31557600 

10314 X 31416 = ^'"^ °' '^^ ""^"^'^^^ '^^ *'^^ 
light employs in traversing a space equal to the dia- 
meter of the earth's orbit, which agrees very nearly 
with the results previously deduced by astronomers 
from observations on the eclipses of Jupiter's satellites. 

The coincidence of these deductions, founded upon 
observations wholly independent of each other is ge- 
nerally considered as furnishing one of the most sa- 
tisfactory proofs of the truths of the Copernican or 
modern system of astronomy. 

13 1 . The aberration S' / lies from the true place of 
a star in a direction parallel to that of the earth's 
motion, and towards the same part ; and its effect 
is therefore produced at one time wholly in decli- 
nation, at another wholly in right ascension, and 
at others, it will effect both these quantities, but in a 
greater or less degree, according to circumstances. 

In order to illustrate this, let E, E', E", E'", (fig. 
42) represent four positions of the earth when the sun 
is in the signs T> Vf, ^, and s, and let tT, ifT', 
t"T", &c. be tangents to the earth's orbit at those 
points ; s, s' the same star seen on the meridian 
of any place. Now in the position E, corresponding 
to the vernal equinox, the sun is in the equator ; 
therefore, if Pnjp be a meridian passing through the 
poles of the equator and ecliptic, Ymp will coincide 
with the solstitial colure, and a line drawn from S to 
E will be perpendicular to the plane of the meridian 
'Pmpn: therefore, if the plane of the ecliptic EE'E", 
be conceived to lie in the plane of the paper, that of 
P)7!p«mustbe perpendicular to it; and SE will be 
also perpendicular to the tangent tT, which tangent, 
therefore, is in the plane of the meridian Fmpn. 

Now the earth being supposed to rotate on its axis 
in the direction n E m, and SE being perpendicular to 
the plane mVpn, the position as shown in the figure 
corresponds to that of 6 o'clock in the evening ; and 
supposing the star s, to be on the meridian at this in- 
stant, it is obvious that it will be situated in a plane 
corresponding with the line of the earth's motion j 
the aberration will therefore produce its effect wholly 
in that plane, and will tend to elevate the star s, from 
s to /, that is, it will increase its declination, or dimi- 
nish its zenith distance ; and it is obvious that a di- 
rectly contrary effect will be produced in the opposite 
position E" corresponding to the autumnal equinox ; 
for the direction of light being then in the line SE", 
while that of the earth is from E" towards i", and 
in the plane of sE^'i" the aberration will be produced 
wholly in the same plane, and \vill tend to depress the 
star; that is, to diminish its declination) or to increase 
its zenith distance. 



Considered 
as a proof 
of the 
earth's re- 
volution. 

Direction 
of aberra' 
tion. 



Fig. 42. 



T R O N O M Y. 



r solstice, 
the meridian 
eridian at 1^ 
^*r'E'i' will be per- 
;ridian ; therefore, 
in a plane passing 
take place in a plane 
the meridian V'n/p^, and 
right or Avest of the 
", the declination of the star, 
such plane, will not be at all 
ascension only, which will be 
opposite position E^'^ corres- 
ter solstice, the effect will still be 
'pt that as the motion of the earth is 
e to that at E', the effect of the aber- 
increase the right ascension of the star, 
■ diminishing it as in the former instance, 
n the particular instances referred to it appears, 
t a star which comes to the meridian at 6 
'ock in the evening, on the 20th March, will be 
ected by aberration only in its declination which 
be increased. 
/ %. That a star which comes to the meridian at 12 
'o'clock at noon, will be affected only in right ascen- 
sion, which will be diminished. 

3. The star which passes the meridian at 6 o'clock 
in the morning, September 23d, will like that which 
passes on March 20 have its declination only affected, 
which in this case will be diminished. 

4. The star which comes upon the meridian at 12 
o'clock at night, Dec. 23, will experience the effect of 
aberration only in right ascension, which will be 
increased. 

Directly the reverse of all this will happen with 
respect to a star whose right ascension is twelve 
hours less than that we have supposed ; for then the 
declination will be diminished in the first case and 
increased in the third ; and the right ascension in- 
creased in the second and diminished in the fourth, 
as is obvious from what is above stated. 

The star T Draconis on which Bradley first made 
his observations, corresponds very nearly in position 
with the supposition in the first case above. 

This particular instance has been selected for 
the pm'pose of showing, that in particular cases the 
effect of aberration may be wholly in right ascension or 
declination ; but generally both these quantities will 
require correction, and consequently also the latitude 
and longitude, and therefore we shall now proceed to 
show how these effects may be separated from each 
other and computed ; in which we shall follow the 
method laid down by professor Vince in his Treatise 
on Astronomy. 

To estimate the effect of aberration in latitude and 
longitude. 

Aberration 132. Let ABCD (fig. 43) be the earth's orbit sup- 
ia latitude posed to be a circle, with the sun in the centre at x ; 
let P X be a line drawn from x perpendicular to ABCD, 
P representing the pole of the ecliptic : let S be the 
true place of the star, and conceive apcq to be the 
circle of aberration parallel to the ecliptic, and abed 
the ellipse into Avhich it is projected; let 7T repre- 
sent an arc of the ecliptic, and draw to it a secondary 
PSG, which will coincide with the minor axis bd. 



and longi- 
tude. 
Fig. 43 



into which the diameter p q is projected. Dra\K 
and it is parallel to pq ; and B.rD perpendicu'tiv^ 
AC, must he parallel to the major axis ac ; tht. 
when the earth is at A, tlie star is in conjunction, and 
in opposition when at C. Now as the place of the 
star in the circle of aberration is always 90° before 
the earth in its orbit, wlien the earth is at A, B, C, D, 
the apparent place of the star in the circle will be at 
a,p, c, q, or in the ellipse at a, b, a, d : hence to find the 
place of the star in the circle when the earth is at any 
point E, take the angle pSs = ExB, and s will be 
the corresponding place of the star in the circle. To 
find its pi'ojected place in the ellipse, draw sv perpen- 
dicular to S c, and v t perpendicular to the same ; in 
the plane of the ellipse join st, and it Avill be pei-pen- 
dicular to v t, because the projection of the circle into 
the ellipse is in lines perpendicular to the latter. 
Draw the secondary PuiK, which will, as to sense, 
coincide with v t ; unless the star be very near the 
pole of the ecliptic ; and the rules here given will be 
sufficiently accurate except in that case. Now as 
c u S is parallel to the ecliptic, S and v must have the 
same latitude, hence vt\s the aberration in latitude ; 
and as G is the true and K the apparent place of the 
star in the ecliptic, GK is the aberration in longitude. 
In order to find these quantities, we may observe, that 
the angle s S c or CtE is the angle of the earth's dis- 
tance from syzygies, and as the angle S2Ji= complement 
of stars latitude, v s t will be the latitude itself. Now 
putting S a, or Ss = r = 20^' the greatest effect of 
aberration ; we have in the right angled triangle Ssv, 

rad =: 1 : sin sS c W r : vs = r sin sS c 
and in the triangle v ts 

1 : sin vst '.'. vs : tv = r sin sSc sin vst 
Therefore, r sin sSc sin v st = aberration in latitude 
Again, in the triangle Ssv, we have 

1 : cos s Sc : r : v s = r cos sSc 
But cos vst : 1 : : Sv : GK 

rcossSc=GK 

or cos vst: 1 '.', r cos sac : • 

cos vst 
the aberration in longitude. 

133. When the earth is in syzygies, sin s S c = o, 
therefore, there is then no aberration in latitude, and 
as cos s S c is then greatest, the aberration in longi- 
tude is at its maximum, as M'e have already explained 
in a particular case with i-eference to declination and 
right ascension. 

"if the earth be at A, or the star in conjunction, 
the apparent place of the star is at a, and reduced to 
the ecliptic at H, therefore GH is the aberration 
which diminishes the longitude of the star, the order 
of the signs being 7, G, T ; but when the earth is at 
C, or the star in opposition, the apparent place c 
reduced to the ecliptic is at F, and the aberration GF 
increases the longitude, hence the longitude is the 
greatest when the star is in opposition, and least when 
in conjunction ; corresponding with what has been 
already shown in a particular case (art. 131) with 
i;espect to the right ascension. 

When the earth is in quadratures at D or B, then cos 
5 S c = 0, and sin s S c is greatest ; there is, therefore, 
then no aberration in longitude, while that in latitude 
is the greatest. When the earth is at D, the apparent 
place of the star is at d, and the latitude is increased, 
but when atB, the apparent place being at b, the lati- 
tude is diminished. Hence the latitude is least in 
4b2 



552 



A S T R O N O ^ Y. 



Astronomy, quadrature before opposition, and greatest in qua- 

^>— — v-i-^ drature after. From the mean of a great number of 

observations, Dr. Bradley determined the value of the 

greatest aberration to be 20" as we have already 

stated (art. 129.) 

Deductions. 134. It follows from what has been shown above, 

1 .That the greatest aberration in latitude is equal to 20" 
multiplied by the sine of the star's latitude, and that 
the aberration in latitude /or anjj time is equal to 20" 
multiplied by the star's latitude and by the sine of the 
elonguticm found for the same time ; and that it is 
subtractive before opposition and additive after it. 

2. The greatest aberration in longitude is equal to 20" 
divided by the cosine of the latitude ; and tlie aberra- 
tion for any time equal to 20" inultiplied by the cosine 
of the elongation, and divided by the cosine of the 
latitude ; it will be subtractive in the first and last 
quadrant of the argument, or of the difference between 
the longitude of the sun and star, and additive in the 
second and third. 

Examples. 
1. Find the greatest aberration of T Ursa Minoris, 
whose latitude is 75° 13'. 
Here sin 75° 13' is -9669 

Mult, by ' 20" , 



20'' 



19"'34 iX\e greatest aberration in lat. 

20" 

- = = 78"' 4 the greatest 

•2551 



^""^ cos 75° 13' 
aberration in longitude. 

2. Required the aberration in latitude and longitude 
of the same star when the earth is 30° from syzygies. 

sin 30° = m = '5 ; hence 

20" X (sin 75° 13') + '5 = 9"'67 aberration 
in latitude ; and since cos 30° = SGQ 

= 67 "89 the aberration in longitude. 

In the case of the sun, weliave always sin sSc =. o 
and cos = 1, also cos lat. = 1 ; and, consequently, 20" 
X sin sSc = 0, or there is no aberration in latitude, 
and the aberration in longitude is constant and equal 
to 20". This quantity 20" of aberration of the sun 
answers to its mean motion in 8' 7"| ; and is there- 
fore the time in which light moves from the sun to 
the earth, at its mean distance, agreeably to what we 
have already stated (art. 130.) Hence the sun always 
appears 20" behind its true place. 

The following table is intended to expedite the calcula- 
tion in the preceding cases. 

The argument for the longitude is long sun — long 
star. The argument for the latitude is long sun — long 
star — 3 signs. 



Degree. 


V[. 


I VII. 


11. VIII. 


Dogree. 




- + 


- + 


— + 







2o'oO 


17-32 


10- 


30 


1 


2000 


17-14 


9-70 


29 


2 


19-99 


lG-96- 


9-39 


28 


3 


19-97 


lG-77 


9- 8 


27 


4 


19-95 


16--58 


8-77 


26 


5 


19-92 


1G-5S 


S-45 


25 



Table. — continiced. 



Degree. 


\\. 


I. VII. 


II. VIII. 


Degree. 




— +\ 


X-" 


— + 




6 


19-89 


^i61S 


8-13 


24 


7 


19-85 


,1^97 


7-81 


23 


8 


19-81 


15-76' 


7-49 


22 


9 


19-75 


15-54 


7-17 


21 


10 


19-70 


15-32 


6-84 


20 


11 


19-63 


15- 9 


6-51 


19 


12 


19-56 


14-86 


6-18 


IS 


13 


19-49 


14-63 


5-85 


17 


14 


19-41 


14-39 


5-51 


16 


15 


19-32 


1414 


518 


15 


16 


19-23 


13-89 


4-84 


14 


17 


19-13 


13-64 


4.50 


13 


18 


19- 2 


13-38 


416 


12 


19 


18-91 


13-12 


3-81 


11 


20 


18-80 


12-86 


3-47 


10 


21 


18-67 


12-59 


3-12 


9 


22 


18-54 


12-21 


2-78 


8 " 


23 


18-41 


12- 4 


2-44 


7 


24 


18-27 


11-76 


2- 9 


6 


25 


18-13 


11-47 


1-74 


5 


26 


17-98 


11-18 


1-40 


4 


27 


17-82 


10-89 


1-50 


3 


28 


17-66 


10-60 


070 


2 


29 


17'49 


1030 


035 


1 


30 


17-32 


10- 


0- 







135. For the aberration in longitude, multiply the AppUcatiois 
corresponding quantities in the table, by the secant of of the table^ 
the star's latitude. 

For the aberration in latitude multiply the quantities 
taken fmm the table by the sine of the star's latitude. 

Example. 

1. Let the longitiule of the sun be 7s 5° 18', the 
longitude of the star 5s. 11° 14', and its latitude 31° 
10' ; to find its aberration in latitude and longitude, 
long. O 7s. 5° 18' 
long. .)(. 5 IS 14' 



1 17 4 correspond in tab. to 13"-62 
see 31° 10' l"-69 

aberration in long. — 15"-92 product 
For the latitude. 

S o / 

long.©— long. .)f = 1 17 4 
— 3 sie-ns 3 



10 17 4 cor. ta . — 14"-65 
1 31° 10 0-5175 



aberration in latitude 



-58 prod. 



To find the aberration in declination and right ascension. 

135'. Let AEL (fig. 44) represent the equator, p its Aberration: 
pole, ACL the ecliptic, P its pole, S the true, place of'" "^'l'^ 



great circles PS a, V sb, pSi 



phv, and hi, bv per- nation. 



/Fig. 44 



nomy- pendicular to pVyVb 

in the preceding articles, we shall have 

^^= tau Ssv 



A S T/R O N O INI Y 

Now ts.aiul vS, be^o' found 



and sinSi'y ; sinSsp '.', Sv 
sin S sp. Sv 



Consequently 

V 10 



sin Hsv. cos dec. 



553 

_ sin Ss/5.Sw Plane 

S < — : — ^ ■ Astronomy. 

suits AD '^ ^ ^ J 

= the aberration 



-which angle hence becomes knowii/ - - ^.^g j^^. 

Again in the triangle Vsp, tM three sides being j„ ,.jg./,^ «icc/;4w» 

given, compute the angle ofposip)nr«;j, and hence liad 137, Notwithstanding the process of solution is 

Sa'p = Sa'u/f Fsp rendered very obvious by the preceding investigation. 

Then again, / it still involves considerable numerical computation, 

„ , . -' . , cosSsp.su to facilitate which, different tables and formula have 

cosSsu : cosSsp .. sv . St = 



been contrived, of which the following, due to De- 
lambre, is deserving of preference. 



cos Ssv 
iberratwn in declination. 

General Tables for the aberration of the fixed stars. 
jSfote. A = right ascension, D the declination of the star, and S = the longitude of the sun 






Table I 


Arg. 


A-S. 




Table I] 


• Arg 


A + S 




Table III. 


Arg. S+D&S-D. 


Signs. 


VI. 


I.-VII. 


II. VIII. 


s. 


S. 


VI. 


L VII. 


II. VIIL 


S. 


S. 


VI. 


I. VII. 


II. VIIL 


s. 


STeg: 


— + 


— + 


— + 


Deg. 


Deg. 


H 


+ — 


+ — 


Deg. 


Deg. 


— 4- 


— + 


— + 


Deg. 





19-17 


16-60 


9-59 


30 





0-83 


0-72 


0-41 


30 





3-98 


3-45 


1-99 


30 


1 


19- 17 


16-43 


9-30 


29 


1 


0-83 


0-71 


0-40 


29 


1 


3-98 


3-42 


1-93 


29 


2 


1916 


16-26 


9-00 


28 


2 


0-82 


070 


0-39 


28 


2 


3 98 


3-38 


1-87 


28 


3 


19- 15 


16-08 


8-70 


27 


3 


0-82 


0-69 


0-38 


27 


3 


3-98 


3-34 


1-81 


27 


4 


1913 


15-89 


8-40 


26 


4 


0-82 


0:68 


0-37 


26 


4 


3-97 


3-30 


1-75 


26 


5 


1910 


15-71 


8-10 


25 


5 


0-82 


0-67 


0-35 


25 


5 


3-97 


3-26 


res 


25 


6 


1907 


15-51 


7-8O 


24 


6 


0-82 


0-67 


0-33 


24 


6 


3-96 


3-22 


1-62 


24 


7 


19-53 


15-31 


7-49 


23 


7 


0-82 


0-66 


0-32 


23 


7 


3-95 


3-18 


1-56 


23 


8 


18-99 


15-11 


7-19 


22 


s 


0-82 


65 


030 


22 


8 


3-94 


3-14 


1-49 


22 


9 


18-94 


14-90 


6-87 


21 


9 


0-82 


0-64 


0-29 


21 


9 


3-93 


3-10 


1-43 


21 


10 


18-88 


14-69 


6-56 


20 


10 


082 


0-63 


0-28 


20 


10 


3-92 


3-05 


1-36 


20 


11 


18-82 


14-47 


6-24 


19 


11 


0-82 


0-62 


0-27 


19 


11 


3-91 


3-10 


1-30 


19 


12 


I8-75 


14-25 


5-93 


18 


12 


0-82 


061 


0-25 


18 


12 


3-90 


2-97 


1-23 


18 


13 


18-68 


1402 


5-61 


17 


13 


0-81 


0-61 


0-24 


17 


13 


3-89 


2-92 


1-17 


17 


14 


18-60 


13-79 


5-28 


16 


14 


081 


0-60 


0-23 


16 


14 


3-87 


2-87 


1-10 


16 


15 


18-52 


13-56 


4-96 


15 


15 


0-80 


0-58 


0-22 


15 


15 


385 


2-82 


1-03 


15 


16 


18-43 


13-32 


4-64 


14 


16 


0-80 


0-57 


020 


14 


16 


3-83 


2-77 


0-97 


14 


17 


18-33 


13-08 


4-31 


13 


17 


0-so 


0-56 


019 


13 


17 


3-81 


2-72 


0-90 


13 


18 


18-23 


12-83 


3-99 


12 


18 


0-79 


0-55 


0-17 


12 


18 


3-79 


2-67 


0-S3 


12 


19 


18-13 


12-56 


3-66 


11 


19 


0-78 


0-54 


0-15 


11 


19 


3-77 


2-62 


0-66 


11 


20 


18-02 


12-32 


3-33 


10 


20 


078 


0-53 


0-14 


10 


20 


3-74 


2-56 


0-69 


10 


21 


17-90 


12-07 


3-00 


9 


21 


0-77 


0-52 


0-12 


9 


21 


3-72 


2-51 


0-63 


9 


22 


17-78 


11-80 


2-67 


8 


22 


0-76 


051 


Oil 


8 


22 


3-70 


2-46 


0-56 


8 


23 


17-65 


11-54 


2-34 


7 


23 


0-76 


0-50 


0-10 


7 


33 


3-67 


2-40 


0-49 


7 


24 


17-52 


11-27 


2-00 


6 


24 


075 


0-49 


0-09 


6 


24 


3-64 


2-34 


0-42 


6 


25 


17-38 


11-00 


1-67 


5 


25 


075 


0-47 


0-07 


5 


25 


361 


2-28 


0-35 


5 


26 


17-23 


10-72 


1-34 


4 


26 


075 


0-46 


0-06 ~ 


4 


26 


3-58 


2-23 


0-28 


4 


27 


I7-O8 


10-44 


1-00 


3 


27 


0-74 


0-45 


0-05 


3 


27 


3-55 


2-17 


0-22 


3 


28 


16-93 


10-16 


67 


2 


28 


073 


0-44 


003 


2 


23 


3-52 


2-11 


014 


2 


29 


16-77 


9-87 


0-33 


1 


29 


0-72 


0-43 


0-02 


1 


29 


3-49 


205 


007 


1 


30 


16-60 


9-59 

1 


000 





30 


0-72 


0-41 


000 





20 


3-45 


1-99 


0-00 





Deg. 


— + 


— + 


h 


Deg. 


Deg. 


-i 


+ — 


-1 


Deg. 


Deg. 


— + 


— + 


h 




Signs 


XL V. 


X. IV. 


IX. III. 


S. 


S. 


XL V. 


X. IV. 


IX. IIL 


s. 


S. 


XL V. 


X. IV. 


IX. III. 





554 



LIBRARY OF CONGRESS 



A S T E O N"\0 M Y. T 



\ 



Use of I 
tables. 



Astronomy. Use of the Tables 

'^ For the aberration in right ascension. 

138. Enter Table J, with the argument A — S, 
and Table 11. with A + S. Then the sum of the two 
corresponding numbers, multiplied by the sec. of D 
will be the aberration in right ascension. 

For the aberration in declination. 

Enter Table I, with the argument A — S + 3 signs, 
and Table II. with A + S + 3 signs, and the sum of 
the two corresponding numbers multiplied by the sine 
of D, Avill be thejirst part of the aberration in decli- 
nation. 

Enter Table III., with the arguments S + D and 
S — D, by which will be found the other two parts of 
the aberration in declination, and the sum of tlie three 
Avill give the whole of the aberration in declinatioii. 

If tiie declination of the star be south, add 6 signs 
to the arguments S + D and S — D. 

EXAJUPLE. 

Required the aberration of a Aquila, Feb. 15, 1819, 
at 1'2 o'clock in the evening. 

Here by the tables, A = 9s 25° 29' D = 8° 24' 25'' 
S = 10 26 2 



Illustrated 
by an ex- 
ample. 



A — S = 10s 29° 27' 
A + S = 8 21 31 



Tab. I.. . - 
Tab. II. . ■ 



-16"- 5 
- 015 



Sec. dec. 8" 24' 25" = 



— 16-6 
10108 



Aberration in right ascen. 16 66 Product 

A— S + 3 signs Is 29° 27' Tab. I. — 1(3"-68 
A + S + 3 signs 11 21 31 Tab. III. + 



0.82 



Sin dec. 8° 24' 25" 
S = 10 2G° 2' 9" 



— 15S6 
■1461 



2-317 



S + D = 11 4° 26' 34'- 
S — D = 10 17 37 44 



Tab. III. — 3'595 
Tab. III. — 2 945 



Aberration in declination — 8-857 
If the declination had been south, the two latter ar- 
guments would have been S -|- D -|- 6 signs, and S 
— D -H 6' signs, as stated above. 

4. Of nutation. 
Nutation, i^q We have in the preceding articles endeavoured 
to illustrate the principles of the most important astro- 
nomical corrections, and have shown the method of 
computation ; there however still remains for expla- 
nation the doctrine of nutation, but as the complete 
developement of tlie principles upon which this theory 
rests, involves considerations of a physical nature 
which we have not hitherto examined, we must in this 
place content ourselves with a very general view of 
the subject, leaving the more minute particulars for 
our treatise on physical astronomy. By nutation is to 
be understood a kind of trepidation or tremulous mo- 
tion of the earth's axis, whereby its inclination to the 
plane of the ecliptic is not always the same ; but vi- 
brates within certain limits, never, however, exceeding 
a few seconds ; the period of variation is also limited 



to a certain number of revoh _ ^ ®03,630 564 2 ^^ , 

orbit. This inequality in the terrestrial motion was, Astronomy' 
like that des-cribed in the foregoing chapter, disco- ^"""V-^A. 
vered by Dr. i^radley, to whom we owe likewise a 
just explanation -of the cause of it, and a near ap- 
proximation of its e-ffects. 

140. We have observed above, that it is impossible Physical 
in this place to give more than a very general expla- cause of. 
nation of this doctrine ; it will be perhaps sufficient 

to observe here, that the first cause of nutation is due 
to the mutual gravitation of matter, and to the laws 
which it is known to observe ; viz. that it is directly 
as the mass, and inversely as the square of the dis- 
tance. If the orbit of the earth were a circle, and 
the terrestrial globe a perfect sphere, the attraction of 
the sun would have no other effect than to keep it in its 
orbit, and would cause no irregularity in the position 
of its axis ; but neither of these conditions takes place, 
the earth is not a perfect sphere, nor is its orbit a circle : 
when the position cf the earth is such, that the plane 
of its equator passes through the centre of the sun, 
the attractive power of the latter body will still have 
no other tendency than that of drawing the earth to- 
wards it, and the parallelism of its axis will not^'? -^ 
disturbed ; this happens in the equinoxes. But as 
the earth recedes from tliese points, the sun deviates 
so much the more from the plane of the equator, and "^ 
the latter, in consequence of its protuberance is more 
powerfully attracted than the rest of tlie globe^ which 
causes soine alteration in its position, that is, in the 
inclination of its axis to the plane of the ecliptic ; and. 
at that part of the orbit, which is described between the 
vernal and autumnal equinox, is less than that passed 
over bet^ve^n the latter and the former ; it follows 
that the irregularity caused by the sun, during its 
passage through the northern signs, is not entirely 
compensated by that which takes place during the 
other part of the revolution ; and consequently, that 
the parallelism of the terrestrial axis, and its inclina- 
tion to the ecliptic will be a little changed. 

141. Again, the same effect which the sun produces Effect of 
upon the earth by its attraction, or at least an analo- the moon, 
gous effect, is also produced by the moon, which is 

more powerful in proportion as it is more distant from 
the equator ; and tlierefore when its nodes concur 
with the equinoctial points, the power which causes 
the irregularity in the position of the terrestrial axis 
acts with tlie greatest force ; and the revolution of 
the moon's nodes being performed in about eighteen 
years, the nodes will twice in this period concur with 
the equinoctial points ; and consequently, twice in 
the same period, or once every nine years, the earth's 
axis will be more influenced than at any other time ; 
and during this interval, the pole of the earth Avill de- 
scribe an ellipse in the heavens, Avhose transverse 
axisisl9"-2, and conjugate axis 15", which corres- 
pond with the ratio between the cosine of the obliquity 
and the cosine of twice the obliquity of the ecliptic ; 
or to the ratio of cos 23° 28' and cos 4G" 56'. 

142. Let TT (fig. 45) be the pole of the ecliptic, and Computed. 
P the mean place of the pole of the equator, ADC a cir- ^'=- ^5* 
cle whose radius is equal to the serai trans\ erse axis of 

the ellipse Crf A described by the pole as above stated, 
A the true pole of the equator when the ascending 
node of the moon's orbit is at T, and let A be supposed 
to move contrary to the order of the signs. Take 



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1 



003 630 564 2 



